2016.9 浙江高考：
One weekend in July, Jane and her husband, Tom, had driven three hours to camp overnight by a lake in the forest. Unfortunately, on the way an unpleasant subject came up and they started to quarrel. By the time they reached the lake, Jane was so angry that she said to Tom. “I'm going to find a better spot for us to camp" and walked away.
With no path to follow,Jane just walked on for quite a long time. After she had climbed to a high place. she turned around, hoping to see the lake. To her surprise, she saw nothing but forest and, far beyond, a snowcapped mountain top. She suddenly realized that she was lost.
“Tom! "she cried. "Help!"
No reply. If only she had not left her mobile phone in that bag with Tom. Jane kept moving, but the farther she walked, the more confused she became. As night was beginning to fall, Jane was so tired that she had to stop for the night. Lying awake in the dark, Jane wanted very much to be with Tom and her family. She wanted to hold him and tell him how much she loved him.
Jane rose at the break of day, hungry and thirsty. She could hear water trickling (滴落）somewhere at a distance. Quickly she followed the sound to a stream. To her great joy,she also saw some berry bushes. She drank and ate a few berries. Never in her life had she tasted anything better. Feeling stronger now. Jane began to walk along the stream and hope it would lead her to the lake.
As she picked her way carefully along the stream, Jane heard a helicopter. Is that for me? Unfortunately, the trees made it impossible for people to see her from above. A few minutes later, another helicopter flew overhead. Jane took off her yellow blouse, thinking that she should go to an open area and flag them if they came back again.
注意:
1.所续写短文的词数应为150左右；
2.应使用5个以上短文文中标有下划线的关键词语：
3.续写部分分为两段，每段的开头语已为你写好；
4.续写完成后，请用下划线标出你所使用的关键词语。
Paragraph 1
But no more helicopters came and it was getting dark again.
Paragraph 2
It was daybreak when Jane woke up.
2017.6
On a bright, warm July afternoon, Mac Hollan, a primary school teacher, was cycling from his home to Alaska with his friends. One of his friends had stopped to make a bicycle repair, but they had encouraged Mac to carry on, and they would catch up with him soon. As Mac pedaled (骑行) along alone, he thought fondly of his wife and two young daughters at home. He hoped to show them this beautiful place someday.
Then Mac heard quick and loud breathing behind him. “Man, that's a big dog!” he thought. But when he looked to the side, h e saw instantly that it wasn’t a dog at all, but a wolf, quickly catching up with him.
Mac’s heart jumped. He found out his can of hear spray. With one hand on the bars, he fired the spray at the wolf. A bright red cloud enveloped the animal, and to Mac's relief, it fell back, shaking its head. But a minute later, it was by his side again. Then it attacked the back of Mac's bike, tearing open his tent bag. He fired at the wolf a second time, and again, it fell back only to quickly restart the chase（追赶）。
Mac was pedaling hard now. He waved and yelled at passing cars but was careful not to show down. He saw a steep uphill climb before him. He knew that once he hit the hill, he’d be easy caught up and the wolf’s teeth would be tearing into his flesh.
At this moment, Paul and Beeky were driving their car on their way to Alaska. They didn’t think much of it when they saw two cyclists repairing their bike on the side of the road. A bit later, they spotted what they, too, assumed was a dog running alongside a man on a bike. As they got closer, they realized that the dog was a wolf. Mac heard a large vehicle behind him. He pulled in front of it as the wolf was catching up fast, just a dozen yards away now.
注意:
1.所续写短文的词数应为150左右；
2.应使用5个以上短文文中标有下划线的关键词语：
3.续写部分分为两段，每段的开头语已为你写好；
4.续写完成后，请用下划线标出你所使用的关键词语。
Paragraph 1
The car abrubtly stopped in front of him.
Paragraph 2
A few minutes later,the other two cyclists arrived.
2017 11. 浙江高考 A vacation with my mother
I had an interesting childhood: It was filled with surprise and amusements, all because of my
I was eleven tells a lot about her.
My two sets of grandparents lived in Colorado and North Dakota, and my parents decided to spend a few weeks driving to those states and seeing all the sights along the way. As the first day
our friends. Who knew if we’d ever see them again? Finally, the moment of our departure arrived,
drove off. We bravely drove off again two hours later after we’d returned home to get the purse
David and I were always a little nervous when using gas station bathrooms if Mom was driving
door and play lookout while you go.” I had terrible pictures in my mind: “Honey, where are the kids?” “What?! Oh, Gosh… I thought they were being awfully quiet.” We were never actually left behind in a strange city, but we weren’t about to take any chances.
for some time, Mom suddenly got a great idea: Why didn’t we find a house with a likely-looking backyard and ask if we could set up tent there? David and I became nervous. To our great relief, Dad turned down the idea. Mom never could understand our objections.If a strange family showed up on her front doorsteps, Mom would have been delighted. She thinks everyone in the world as
注意：
1. 所续写短文的词数应为150左右；
2. 应使用5个以上短文中标有下划线的关键词语；
3. 续写部分分为两段，每段开头语已为你写好；
4. 续写完成后，请用下划线标出你所使用的关键词语。
Para1: The next day we remembered the brand-new tent we had brought with us. Para2: We drove through several states and saw lots of great sights along the way.
2018 6
It was summer, and my dad wanted to treat me to a vacation like never before. He decided to take me on a trip to the Wild West.
We took a plane to Albuquerque, a big city in the state of New Mexico. We reached Albuquerque in the late afternoon. Uncle Paul, my dad’s friend, picked us up from the airport and drove us up to his farm in Pecos.
His wife Tina cooked us a delicious dinner and we got to know his sons Ryan and Kyle. My dad and I spent the night in the guestroom of the farm house listening to the frogs and water rolling down the river nearby. Very early in the morning, Uncle Paul woke us up to have breakfast. "The day starts at dawn on my farm," he said. After breakfast, I went to help Aunt Tina feed the chickens. while my dad went with Uncle Paul to take the sheep out to graze(吃草). I was impressed to see my dad and Uncle Paul riding horses. They looked really cool.
In the afternoon, I asked Uncle Paul if I could take a hose ride, and he said yes, as long as my dad went with me. I wasn’t going to take a horse ride by myself anyway. So, my dad and I put on our new cowboy hats, got on our horses, and headed slowly towards the mountains. "Don’t be late for supper," Uncle Paul cried, "and keep to the track so that you don’t get lost!" "OK! " my dad cried back. After a while Uncle Paul and his fam house were out of sight. It was so peaceful and quiet and the colors of the brown rocks, the deep green pine trees, and the late afternoon sun mixed to create a magic scene. It looked like a beautiful woven(编织的）blanket spread out upon the ground just for us.
注意：
1. 所续写短文的词数应为l50左右；
2. 至少使用5个短文中标有下划线的关键词语：
3. 续写部分分为两段，每段的开头语已为你写好；
4. 续写完成后，请用下划线标出你所使用的关键词语。
Suddenly a little rabbit jumped out in front of my horse.
We had no idea where we were and it got dark.
参考范文一：
Paragraph 1
But no more helicopters came and it was getting dark again. Jane had to stay alone in the forest for another cold night. At that moment (时间), she felt a little sad, but she wasn’t so frightened (情感). She reminded herself constantly, (心理) “Tom must have called for those helicopters. Maybe (情感) he was in one of them and will return soon(动作)! I have to guide him tomorrow.” She felt asleep (动作) and dreamed of seeing Tom (动作).
Paragraph 2
It was daybreak when Jane woke up. She ate some berries and then(时间) walked along the stream, hoping (心理) to find a suitable place to guide the helicopter. She walked and walked, exhausted but full of hope. Suddenly (时间), she spotted (动作) a huge flat rock. She managed (动作) to climb onto it and waited with patience. The moment (时间) the helicopter appeared (动作) again. The nearer it got (动作), the more she waved (动作) the yellow blouse. To her great joy, (情感) the helicopter didn’t miss Jane this time and it landed near the big rock slowly. Tom jumpe d off the helicopter and rushed (动作) towards Jane. They hugged each other tightly (情感) and burst into tears (情感).
参考范文二：
of the car. It was locked. He then ran around to the passenger door, but it was locked, as well, so he began to climb through the open window. When spotting this ,Paul quickly unlocked the door,
A few minutes later, the other two cyclists arrived .Mac emerged from the car and hugged his friends. “I thought I was going to die,” Mac cried to them. Mac retrieved（取回）his bicycle, and the three men resumed(继续）their road trip, agreeing to keep in one another’s sight line. A few miles down the road, Mac pulled over and burst into tears.“The rest of the trip was amazing, but I had to let the former emotion o ut.”
参考范文三：
Para1: The next day we remembered the brand-new tent we had brought with
wise as I admiring our stunning tent. “Oh, I forgot the pillows!” what a misconception. Despite the ache of my neck, we had some great nights.
Para1: We drove through several states and saw lots of great sights along the
way. The bright blue sky, the limitless green grass, the group of sheep, the setting sun and the countless stars in the curtain of nights kept me spellbound. Not only did we
see the picturesque scenery, we also managed to consider mom’s scandals as a kind of fun. I really love my Mum.
To our relief, we arrived at grandparents’ place and went back to our home with all of four people. It was so fortunate to see my friends again.
范文四：
Paragraph 1
Suddenly a little rabbit jumped out in front of my horse. Instinctively, I yelled out loud, pulling back the reins hard in order to stop the horse from hurting the little creature. Badly startled by the sudden incident, the horse sped off the track into another direction. Dad followed closely behind, calling out to tell me how to soothe the terrified horse and I did as told. Finally, the horse calmed down, but we seemed to get lost, unable to go back to the mountain road.
Paragraph 2
We had no idea where we were and it was getting dark. Wandering around, we were still stuck in the dilemma. Much to our delight, the sound of water in the distance caught our attention and drove us to the riverbank. Dad proposed that we should walk along the river which may lead us to the farm house and nothing seemed better than that. Time appeared to be merrier and shorter when I
stayed together with Dad and before long, the farm house came into sight. What a thrilling but memorable experience it was!
Version 2
Suddenly a little rabbit jumped out in front of my horse. I immediately grew fond of the furry r abbit and called out excitedly, “Dad! Look!” Alarmed, the rabbit ran away in a flash. I followed it eagerly, hoping to catch it as my trophy for the trip. My dad just followed me, knowing it was impossible to stop me. We tracked the rabbit for about ten minutes until it got completely out of sight. Depressed and tired, I suggested going back. But apparently, we had diverged from the track Uncle Paul warned us to keep. (86 words)
We had no idea where we were and it was getting dark. The thought that we might have got lost in such darkness sent shivers down my spine. Tears of fear and regret filled my eyes. Fortunately, Dad was not so panicked as I was. He kept silent and listened very carefully as he took my horse rein and led the way. We had wandered for what seemed like ages when suddenly a river came into sight. Hopefully, we could find our way back to the farm house if we followed the river. Finally, we arrived home safely just in time for supper, but what an experience! It turns out there’s always a way out of any plight(困境）as long as we stay calm. (114 words)
高考大题之解析几何 1.如图，椭圆C ：22221x y a b +=(a >b >0)的离心率e =3 5 ，左焦点为F ，A ，B ，C 为其三个顶 点，直线CF 与AB 交于点D ，若△ADC 的面积为15． (Ⅰ)求椭圆C 的方程； (Ⅱ)是否存在分别以AD ，AC 为弦的两个相外切的等圆？ 若存在，求出这两个圆的圆心坐标；若不存在，请说明理由． 解：(Ⅰ)设左焦点F 的坐标为(-c ，0)，其中c =22a b -， ∵e = 35c a =，∴a =5 3 c ，b =43c ． ∴A (0，43c )，B (-5 3c ，0)，C (0，-43c )， ∴AB ：33154x y c c -+=，CF ：314x y c c --=， 联立解得D 点的坐标为(-54c ，1 3c )． ∵△ADC 的面积为15，∴12|x D |·|AC |=15，即12·54c ·2·4 3 c =15， 解得c =3，∴a =5，b =4，∴椭圆C 的方程为22 12516 x y +=． (Ⅱ)由(Ⅰ)知，A 点的坐标为(0，4)，D 点的坐标为(-15 4 ，1)． 假设存在这样的两个圆M 与圆N ，其中AD 是圆M 的弦，AC 是圆N 的弦， 则点M 在线段AD 的垂直平分线上，点N 在线段AC 的垂直平分线y =0上． 当圆M 和圆N 是两个相外切的等圆时，一定有A ，M ，N 在一条直线上，且AM =AN ． ∴M 、N 关于点A 对称，设M (x 1，y 1)，则N (-x 1，8-y 1)， 根据点N 在直线y =0上，∴y 1=8．∴M (x 1，8)，N (-x 1，0)， 而点M 在线段AD 的垂直平分线y -52=-54(x +158)上，可求得x 1=-251 40 . 故存在这样的两个圆，且这两个圆的圆心坐标分别为 M (-25140，8)，N (25140 ，0)． 2.如图，椭圆22 221(0)x y a b a b +=>>的左焦点为F ，过点F 的直线交椭圆于B A ,两点， AF 的最大值为M ，BF 的最小值为m ，满足2 34 M m a ?= 。 （Ⅰ）若线段AB 垂直于x 轴时，3 2 AB = ，求椭圆的方程； （Ⅱ） 设线段AB 的中点为G ，AB 的垂直平分线与x 轴和y 轴分别交于E D ,两
高考读后续写训练1. Name________________ It had been some time since Jack had seen the old man. College, career, and life itself got in the way. In fact, Jack moved clear across the country in pursuit (追寻) of the dreams. There, in the rush of his busy life, Jack had little time to think about the past and often no time to spend with his wife and son. He was working on his future, and nothing could stop him. Over the phone, his mother told him, “Mr. Belser died last night. The funeral（葬礼）is Wednesday.” Memories flashed（闪现）through his mind like an old newsreel (新闻短片) as he sat quietly remembering his childhood days. “Jack, did you hear me?” “Oh, sorry, Mom. Yes, I heard you. It’s been so long since I thought of him. I’m sorry, but I honestly thought he died years ago,” Jack said. “Well, he didn’t forget you. Every time I saw him he’d ask how you were doing. He’d reminisce (回忆) about the many days you spent over ‘his side of the fence’ as he put it, ” Mom told him. “I loved that old house he lived in,” Jack said. “You know, Jack, after your father died, Mr. Belser stepped in to make sure you had a man’s influence (影响) in your life,” she said. “He’s the one who taught me carpentry. I wouldn’t be in this business if it weren’t for him. He spent a lot of time teaching me things that he thought were important. Mom, I’ll be there for the funeral.” Jack said. Busy as he was, he kept his word. Jack caught the next flight to his hometown. Mr. Belser’s funeral was small and uneventful. He had no children of his own, and most of his relatives had passed away. The night before he had to return home, Jack and his Mom stopped by to see the old house next door one more time, which was exactly as he remembered. Every step held memories. Every picture, every piece of furniture … Jack stopped suddenly. “What’s wrong, Jack?” his Mom asked. “The box is gone,” he said. “What box?” Mom ask ed. “There was a small gold box that he kept locked on top of his desk. I must have asked him a thousand times what was inside. All he’d ever tell me was ‘the thing I value most’,” Jack said. It was gone. Everything about the house was exactly how Jack remembered it, except for the box. He figured someone from the Belser family had taken it. “Now I’ll never know what was so valuable to him,” Jack said sadly. 1.所续写短文的词数应为150左右； 2.应使用5个以上短文中标有下划线的关键词语； 3.续写部分分为两段，每段的开头已为你写好； 4.续写完成后，请用下划线标出你所使用的关键词语。
2005-2017年浙江高考理科数学历年真题之解析几何大题 （教师版） 1、（2005年）如图，已知椭圆的中心在坐标原点，焦点12,F F 在x 轴上，长轴12A A 的长为4，左准线l 与x 轴的交点为M ，|MA 1|∶|A 1F 1|＝2∶1． (Ⅰ)求椭圆的方程； (Ⅱ)若直线1l ：x ＝m (|m |＞1)，P 为1l 上的动点，使12F PF ∠ 最大的点P 记为Q ，求点Q 的坐标(用m 表示)． 解析：(Ⅰ)设椭圆方程为()22 2210x y a b a b +=>>，半焦距为c ， 则2111,a MA a A F a c c =-=- ，()2 222 224 a a a c c a a b c ?-=-??? =??=+???由题意,得 2,1a b c ∴=== ，22 1.43 x y +=故椭圆方程为 (Ⅱ) 设()0,,||1P m y m >，当00y >时，120F PF ∠=； 当00y ≠时，22102 F PF PF M π <∠<∠<，∴只需求22tan F PF ∠的最大值即可 设直线1PF 的斜率011y k m = +，直线2PF 的斜率0 21 y k m =-， 021********||tan 11y k k F PF k k m y -∴∠= =≤=+-+ 0||y =时，12F PF ∠ 最大，(,,||1Q m m ∴> 2、（2006年）如图，椭圆b y a x 222+＝1（a ＞b ＞0）与过点A （2，0）、B(0,1)的直线有且只有一个公共点T ， 且椭圆的离心率e= 2 3。 (Ⅰ)求椭圆方程； (Ⅱ)设F 1、F 2分别为椭圆的左、右焦点，M 为线段AF 2的中点，求证：∠ATM=∠AF 1T 。
浙江高考历年真题之解析几何大题 1、（2005年）如图，已知椭圆的中心在坐标原点，焦点12,F F 在x 轴上，长轴12A A 的长为4，左准线l 与x 轴的交点为M ，|MA 1|∶|A 1F 1|＝2∶1． (Ⅰ)求椭圆的方程； (Ⅱ)若直线1l ：x ＝m (|m |＞1)，P 为1l 上的动点，使12F PF ∠ 最大的点P 记为Q ，求点Q 的坐标(用m 表示)． 解析：(Ⅰ)设椭圆方程为()22 2210x y a b a b +=>>，半焦距为c ， 则2111,a MA a A F a c c =-=- ，()2 222 224 a a a c c a a b c ?-=-??? =??=+??? 由题意,得 2,3,1a b c ∴=== ，22 1.43 x y +=故椭圆方程为 (Ⅱ) 设()0,,||1P m y m >，当00y >时，120F PF ∠=； 当00y ≠时，22102 F PF PF M π <∠<∠<，∴只需求22tan F PF ∠的最大值即可设直线1PF 的斜率011y k m = +，直线2PF 的斜率0 21 y k m =-， 002122222212002||tan 1121||1 y k k F PF k k m y m y m -∴∠= =≤= +-+-?- 2 01||m y -=时，12F PF ∠最大，(2,1,||1Q m m m ∴±->
2、（2006年）如图，椭圆b y a x 2 22+＝1（a ＞b ＞0）与过点A （2，0）、B(0,1)的直线有且只有一个公共点T ，且椭圆的 离心率e= 2 3 。 (Ⅰ)求椭圆方程； (Ⅱ)设F 1、F 2分别为椭圆的左、右焦点，M 为线段AF 2的中点，求证：∠ATM=∠AF 1T 。 解析：（Ⅰ）过 A 、B 的直线方程为 12 x y += 因为由题意得??? ????+-==+1211 2222x y b y a x 有惟一解， 即0)4 1(22222 22 =-+-+ b a a x a x a b 有惟一解, 所以22 2 2 (44)0(0),a b a b ab ?=+-=≠故442 2 -+b a =0; 又因为e 3 c =即 22234 a b a -= ， 所以2 2 4a b = ;从而得22 1 2,,2 a b == 故所求的椭圆方程为22212x y += （Ⅱ）由（Ⅰ）得6c = , 所以 1266((F F ，从而M （1+4 6 ，0） 由 ?? ???+-==+1 211222 2x y y x ，解得 121,x x == 因此1(1,)2T = 因为126tan 1-= ∠T AF ，又21 tan =∠TAM ，6 2tan =∠2TMF ，得 12 6 6 1 121 62 tan -= + -= ∠ATM ，因此，T AF ATM 1∠=∠ 3、（2007年）如图，直线y kx b =+与椭圆2 214 x y +=交于A B ，两点，记AOB △的面积为S ．
2016.9 浙江高考： One weekend in July, Jane and her husband, Tom, had driven three hours to camp overnight by a lake in the forest. Unfortunately, on the way an unpleasant subject came up and they started to quarrel. By the time they reached the lake, Jane was so angry that she said to Tom. “I'm going to find a better spot for us to camp" and walked away. With no path to follow,Jane just walked on for quite a long time. After she had climbed to a high place. she turned around, hoping to see the lake. To her surprise, she saw nothing but forest and, far beyond, a snowcapped mountain top. She suddenly realized that she was lost. “Tom! "she cried. "Help!" No reply. If only she had not left her mobile phone in that bag with Tom. Jane kept moving, but the farther she walked, the more confused she became. As night was beginning to fall, Jane was so tired that she had to stop for the night. Lying awake in the dark, Jane wanted very much to be with Tom and her family. She wanted to hold him and tell him how much she loved him. Jane rose at the break of day, hungry and thirsty. She could hear water trickling (滴落）somewhere at a distance. Quickly she followed the sound to a stream. To her great joy,she also saw some berry bushes. She drank and ate a few berries. Never in her life had she tasted anything better. Feeling stronger now. Jane began to walk along the stream and hope it would lead her to the lake. As she picked her way carefully along the stream, Jane heard a helicopter. Is that for me? Unfortunately, the trees made it impossible for people to see her from above. A few minutes later, another helicopter flew overhead. Jane took off her yellow blouse, thinking that she should go to an open area and flag them if they came back again. 注意: 1.所续写短文的词数应为150左右； 2.应使用5个以上短文文中标有下划线的关键词语： 3.续写部分分为两段，每段的开头语已为你写好； 4.续写完成后，请用下划线标出你所使用的关键词语。 Paragraph 1 But no more helicopters came and it was getting dark again.
高考中解析几何的常考题型分析 一、高考定位 回顾2008,2012年的江苏高考题，解析几何是重要内容之一，所占分值在25 分左右，在高考中一般有2,3条填空题，一条解答题.填空题有针对性地考查椭圆、双曲线、抛物线的定义、标准方程和简单几何性质及其应用，主要针对圆锥曲线本身，综合性较小，试题的难度一般不大;解答题主要是以圆或椭圆为基本依托，考查椭圆方程的求解、考查直线与曲线的位置关系，除了本身知识的综合，还会与其它知识如向量、函数、不等式等知识构成综合题，多年高考压轴题是解析几何题. 二、应对策略 复习中，一要熟练掌握椭圆、双曲线、抛物线的基础知识、基本方法，在抓住通性通法的同时，要训练利用代数方法解决几何问题的运算技巧. 二要熟悉圆锥曲线的几何性质，重点掌握直线与圆锥曲线相关问题的基本求解方法与策略，提高运用函数与方程思想、向量与导数的方法来解决问题的能力. 三在第二轮复习中要熟练掌握圆锥曲线的通性通法和基本知识. 预测在2013年的高考题中: 1.填空题依然是直线和圆的方程问题以及考查圆锥曲线的几何性质为主，三种圆锥曲线都有可能涉及. 2.在解答题中可能会出现圆、直线、椭圆的综合问题，难度较高，还 有可能涉及简单的轨迹方程和解析几何中的开放题、探索题、证明题，重点关注定值问题. 三、常见题型
1.直线与圆的位置关系问题 直线与圆的位置关系是高考考查的热点，常常将直线与圆和函数、三角、向量、数列、圆锥曲线等相互交汇，求解参数、函数最值、圆的方程等，主要考查直线与圆的相交、相切、相离的判定与应用，以及弦长、面积的求法等，并常与圆的几何性质交汇，要求学生有较强的运算求解能力. 求解策略:首先，要注意理解直线和圆等基础知识及它们之间的深入联系;其次，要对问题的条件进行全方位的审视，特别是题中各个条件之间的相互关系及隐含条件的挖掘;再次，要掌握解决问题常常使用的思想方法，如数形结合、化归转化、待定系数、分类讨论等思想方法;最后，要对求解问题的过程清晰书写，准确到位. 点评:(1)直线和圆的位置关系常用几何法，即利用圆的半径r，圆心到直线的距离d及半弦长l2构成直角三角形关系来处理. (2)要注意分类讨论，即对直线l分为斜率存在和斜率不存在两种情况分别研究，以防漏解或推理不严谨. 2.圆锥曲线中的证明问题 圆锥曲线中的证明问题，主要有两类:一类是证明点、直线、曲线等几何元素中的位置关系，如:某点在某直线上、某直线经过某个点、某两条直线平行或垂直等;另一类是证明直线与圆锥曲线中的一些数量关系(相等或不等). 求解策略:主要根据直线、圆锥曲线的性质、直线与圆锥曲线的位置关系等，通过相关的性质应用、代数式的恒等变形以及必要的数值计算等进行证明. 常用的一些证明方法: 点评:本题主要考查双曲线的概念、标准方程、几何性质及其直线与双曲线的关系.特别要注意直线与双曲线的关系问题，在双曲线当中，最特殊的为等轴双曲
2016浙江精彩题选——解析几何解答题 1.（2016名校联盟第一次）19．（本题满分15分） 已知椭圆C ：22 a x ＋y 2b 2＝1(a >b >0)的左右焦点为F 1,F 2 ，离心率为e .直线l :y =ex +a 与x 轴、y 轴分别交于点A ,B 两点，M 是直线l 与椭圆C 的一个公共点，P 是点F 1关于直线 l 的对称点，设. （Ⅰ）若l = 3 4 ，求椭圆C 的离心率； （Ⅱ）若D PF 1F 2 为等腰三角形，求l 的值.
2.（2016温州一模19）．（本题满分15分）如图，已知椭圆C： 22 22 1(0) x y a b a b +=>> 经过点 ,A B分别为椭圆C的左、右顶点，N M,是椭圆C上非顶点的两点，且OMN ?的面积等于2．（Ⅰ）求椭圆C的方程； （Ⅱ）过点A作OM AP//交椭圆C于点P，求证：ON BP//． 解：（Ⅰ）由题意得： ? ? ? ? ? ? ? ? ? ? ? + = = = = + 2 2 2 2 2 2 2 2 1 ) 2 6 ( 1 c b a a c e b a ，解得： ?? ? ? ? = = 2 4 2 2 b a 故椭圆C的方程为：1 2 4 2 2 = + y x ……………………………………5分 （Ⅱ）解法一：如图所示，设直线OM,ON的方程为 OM y k x =， ON y k x = 联立方程组22 1 42 OM y k x x y = ? ? ? += ?? ，解得M, 同理可得( N,……………………………………7分作' MM x ⊥轴, ' NN x ⊥轴,',' M N是垂足, OMN S ? = '' ''OMM ONN MM N N S S S ?? -- 梯形 1 [()()] 2M N M N M M N N y y x x x y x y =+--+ 1 () 2M N N M x y x y =- 1 2 = =9分 已知 OMN S ? 2 =，化简可得 2 - = ON OM k k.……………………………………11分 设(,) P P P x y,则22 42 P P x y -=，
浙江高考英语读后续写 第二节读后续写（满分25分） 阅读下面短文,根据所给情节进行续写,使之构成一个完整的故事 “I’m going to miss you so much, Poppy,” said the tall, thin teenager. He bent down to hug his old friend goodbye. He stood up, hugged his parents, and smiled, trying not to let his emotions （情绪）get the better of him. His parents were not quite able to keep theirs under control. They had driven their son several hours out of town to the university where he would soon be living and studying. It was time to say goodbye for now at least. The family hugged and smiled through misty eyes and then laughed. The boy lifted the last bag onto his shoulder, and flashed a bright smile. “I guess this is it,” he said. “I’ll see you back home in a month, okay” His parents nodded, and they watched as he walked out of sight into the crowds of hundreds of students and parents. The boy’s mother turned to the dog, “Okay, Poppy, time to go back home.” The house seemed quiet as a tomb without the boy living there. All that week, Poppy didn’t seem interested in her dinner, her favorite toy, or even in her daily walk. Her owners were sad too, but they knew their son would be back to visit. Poppy didn’t. & They offered the dog some of her favorite peanut butter treats. They even let her sit on the sofa, but the old girl just wasn’t her usual cheerful self. Her owners started to get worried. “What should we do to cheer Poppy up” asked Dad. “We’ve tried everything.” “I have an idea, but it might be a little crazy,”smiled Mom. “Without anybody left in the house but us, this pla ce could use a bit of fun. Let’s get a little dog for Poppy. It didn’t take long before they walked through the front door carrying a big box. Poppy welcomed them home as usual but when she saw the box, she stopped. She put her nose on it. Her tail began wagging（摆动）ever so slowly, then faster as she caught the smell. 注意: 1.所续写短文的词数应为150左右; 2.至少使用5个短文中标有下划线的关键词语; 3.续写部分分为两段, 每段的开头语已为你写好; 4.续写完成后, 请用下划线标出你所使用的关键词语。 Para 1. Dad opened the box and a sweet little dog appeared. 》 Para 2. A few weeks later, the boy arrived home from university. Dad opened the box and a sweet little dog appeared. Then out of the box jumped a small mass of golden woolen thing, shouting loudly and joyfully, as if he was asking why he couldn’t see the sunshine for such a long time. Finding that she had a playmate again, Poppy was amazed. She appreciated her new little playmate, smiling amusedly, barking gently, walking slowly around it and wagging her tail cheerfully and constantly. “I don't have to be
1. 设抛物线22(0)y px p =>的焦点为F ，点(0,2)A .若线段FA 的中点B 在抛物线上， 则B 到该抛物线准线的距离为_____________。（3分） 2 .已知m ＞1，直线2:02m l x my --=，椭圆2 22:1x C y m +=，1,2F F 分别为椭圆C 的左、 右焦点. （Ⅰ）当直线l 过右焦点2F 时，求直线l 的方程；（Ⅱ）设直线l 与椭圆C 交于,A B 两点，12AF F V ，12BF F V 的重心分别为 ,G H .若原点O 在以线段GH 为直径的圆内，求实数m 的取值范 围.（6分） 3已知以原点O 为中心，) F 为右焦点的双曲线C 的离心率2 e = 。 （I ） 求双曲线C 的标准方程及其渐近线方程； （II ） 如题（20）图，已知过点()11,M x y 的直线111:44l x x y y +=与过点 ()22,N x y （其中2x x ≠）的直 线222:44l x x y y +=的交点E 在双曲线C 上，直线MN 与两条渐近线分别交与G 、H 两点，求OGH ?的面积。（8分）
4.如图，已知椭圆 22 22 1(0)x y a b a b +=＞＞的离心率为2，以该椭圆上的点和椭圆的左、右 焦点12,F F 为顶点的三角形的周长为1).一等轴双曲线的顶点是该椭圆的焦点，设P 为该双曲线上异于顶点的任一点，直线1PF 和2PF 与椭圆的交点分别为B A 、和C D 、. （Ⅰ）求椭圆和双曲线的标准方程；（Ⅱ）设直线1PF 、 2PF 的斜率分别为1k 、2k ，证明12·1k k =；（Ⅲ）是否存在常数λ，使得 ·A B C D A B C D λ +=恒成立？若存在，求λ的值；若不存在，请说明理由.（7分） 5.在平面直角坐标系xoy 中，如图，已知椭圆15 922=+y x
2016~2020浙江省高考读后续写 1.（2016年10月，浙江高考） One weekend in July,Jane and her husband,Tom, had driven three hours to camp overnight by a lake in the forest. Unfortunately, on the way an unpleasant subject came up and they started to quarrel. By the time they reached the lake, Jane was so angry that she said to Tom. “I’m going to find a better spot for us to camp” and walked away. With no path to follow, Jane just walked on for quite a long time. After she had climbed to a high place, she turned around, hoping to see the lake. To her surprise, she saw nothing but forest and, far beyond, a snowcapped mountain top. She suddenly realized that she was lost. “Tom! ”she cried. “Help!” No reply. If only she had not left her mobile phone in that bag with Tom. Jane kept moving, but the farther she walked, the more confused she became. As night was beginning to fall, Jane was so tired that she had to stop for the night. Lying awake in the dark, Jane wanted very much to be with Tom and her family. She wanted to hold him and tell him how much she loved him. Jane rose at the break of day, hungry and thirsty. She could hear water trickling (滴落）somewhere at a distance. Quickly she followed the sound to a stream.To her great joy, she also saw some berry bushes. She drank and ate a few berries. Never in her life had she tasted anything better. Feeling stronger now, Jane began to walk along the stream and hope it would lead her to the lake. As she picked her way carefully along the stream, Jane heard a helicopter.Is that for me? Unfortunately, the trees made it impossible for people to see her from above. A few minutes later, another helicopter flew overhead. Jane took off her yellow blouse, thinking that she should go to an open area and flag them if they came back again. 注意： 1. 所续写短文的词数应为l50左右； 2. 至少使用5个短文中标有下划线的关键词语； 3. 续写部分分为两段，每段的开头语已为你写好； 4. 续写完成后，请用下划线标出你所使用的关键词语。 Paragraph 1： But no more helicopters came and it was getting dark again. ____________________________________________________________________________________________ Paragraph 2: It was daybreak when Jane woke up. ____________________________________________________________________________________________【解析】 ◆题型解读 读后续写要求考生首先要读懂已有信息，不仅能读懂字面含义，还要理清文章的脉络和关系。续写这篇短文时，考生需要明白故事的发展进程、前因后果、地理位置变化、人物特征和情感等。在此基础上，考生顺着文章的思路，根据线索，发挥想象，对其后的情节进行合理预测，并用英语表达出来。同时，在组织语言时，切记使用5个以上给出的提示词。 ◆故事主线
解析几何大题二 1．椭圆M 的中心在坐标原点O ，左、右焦点F 1，F 2在x 轴上，抛物线N 的顶点也在原点O ，焦点为F 2，椭圆M 与抛物线N 的一个交点为A （3，2）． （Ⅰ）求椭圆M 与抛物线N 的方程； （Ⅱ）在抛物线M 位于椭圆内（不含边界）的一段曲线上，是否存在点B ，使得△AF 1B 的外接圆圆心在x 轴上？若存在，求出B 点坐标；若不存在，请说明理由． 2．已知椭圆22 22:1(0)x y C a b a b +=>>的右焦点F 到直线30x y -+=的距离为22，231,P ?? ? ? ?? 在椭圆C 上. （1）求椭圆C 的方程； （2）若过F 作两条互相垂直的直线12,l l ，,A B 是1l 与椭圆C 的两个交点，,C D 是2l 与椭圆C 的两个交点，,M N 分别是线段,AB CD 的中点试，判断直线MN 是否过定点？若过定点求出该定点的坐标；若不过定点，请说明理由. 3．已知抛物线C:y 2 =2px(p>0)的焦点F 和椭圆22 143 x y +=的右焦点重合,直线过点F 交抛物线于A 、 B 两点. (1)求抛物线C 的方程； (2)若直线交y 轴于点M,且,MA mAF MB nBF ==u u u r u u u r u u u r u u u r ,m 、n 是实数,对于直线,m+n 是否为定值? 若是,求出m+n 的值；否则,说明理由. 4．已知椭圆22 22:1(0)x y E a b a b +=>>的上顶点为B ，点(0,2)D b -，P 是E 上且不在y 轴上的点， 直线DP 与E 交于另一点Q .若E 的离心率为2 2，PBD ?的最大面积等于 322 . （1）求E 的方程； （2）若直线,BP BQ 分别与x 轴交于点,M N ，判断OM ON ?是否为定值.
历年浙江解析几何高考题 1、（042）直线y=2与直线x+y—2=0的夹角是（） (A)(B)(C)(D) 2、（046文理）曲线y2=4x关于直线x=2对称的曲线方程是（） (A)y2=8--4x (B)y2=4x—8 (C)y2=16--4x (D)y2=4x—16 3、(0411文理)椭圆的左、右焦点分别为F1、F2，线段F1F2被点（，0） 分成5：3两段，则此椭圆的离心率为（） (A)(B)(C)(D) 4、（0422文理）（本题满分14分）已知双曲线的中心在原点，右顶点为A（1，0）.点P、Q 在双曲线的右支上，点M（m,0）到直线AP的距离为1. （Ⅰ）若直线AP的斜率为k ，且，求实数m的取值范围； （Ⅱ）当时，ΔAPQ的内心恰好是点M，求此双曲线的方程. 5、（053文理）．点(1，－1)到直线x－y＋1＝0的距离是( ) (A) (B) (C) (D) 6、（059）．函数y＝ax2＋1的图象与直线y＝x相切，则a＝( ) (A)1/8 (B)1/4 (C) 1/2 (D)1 7、（0513文理）．过双曲线(a＞0，b＞0)的左焦点且垂直于x轴的直线与双曲线 相交于M、N两点，以MN为直径的圆恰好过双曲线的右顶点，则双曲线的离心率等于_________．
8、（0519）．如图，已知椭圆的中心在坐标原点，焦点F 1，F 2 在x轴上，长轴A 1 A 2 的长为4， 左准线l与x轴的交点为M，|MA 1|∶|A 1 F 1 |＝2∶1． (Ⅰ)求椭圆的方程； (Ⅱ)若点P为l上的动点，求∠F 1PF 2 最大值． （理）(Ⅱ)若直线l1：x＝m(|m|＞1)，P为l1上的动点，使∠F1PF2最大的点P记为Q，求点Q的坐标(用m表示)． 9、(063)抛物线的准线方程是（） (A) (B) (C) (D) 10、（0613）双曲线上的离心率是3，则等于 11、（0619）如图，椭圆＝1（a＞b＞0）与过点A（2，0）B(0,1)的直线有且只有一个公共点T，且椭圆的离心率e=(Ⅰ)求椭圆方程； (Ⅱ)设F、F分别为椭圆的左、右焦点，求证：。 （理Ⅱ）设、分别是椭圆的左、右焦点，为线段的中点，求证；
解析几何解答题 1、椭圆G ：)0(122 22>>=+b a b y a x 的两个焦点为F 1、F 2，短轴两端点B 1、B 2，已知 F 1、F 2、B 1、B 2四点共圆，且点N （0，3）到椭圆上的点最远距离为.25 （1）求此时椭圆G 的方程； （2）设斜率为k （k ≠0）的直线m 与椭圆G 相交于不同的两点E 、F ，Q 为EF 的中点，问E 、F 两点能否关于 过点P （0， 3 3）、Q 的直线对称若能，求出k 的取值范围；若不能，请说明理由． ; 2、已知双曲线221x y -=的左、右顶点分别为12A A 、，动直线:l y kx m =+与圆22 1x y +=相切，且与双曲线左、右两支的交点分别为111222(,),(,)P x y P x y . （Ⅰ）求k 的取值范围，并求21x x -的最小值； （Ⅱ）记直线11P A 的斜率为1k ，直线22P A 的斜率为2k ，那么，12k k ?是定值吗证明你的结论. @ [
3、已知抛物线2 :C y ax =的焦点为F ，点(1,0)K -为直线l 与抛物线C 准线的交点，直线l 与抛物线C 相交于A 、 B 两点，点A 关于x 轴的对称点为D ． （1）求抛物线 C 的方程。 ~ （2）证明：点F 在直线BD 上； （3）设8 9 FA FB ?=，求BDK ?的面积。． { — 4、已知椭圆的中心在坐标原点O ，焦点在x 轴上，离心率为1 2 ，点P （2，3）、A B 、在该椭圆上，线段AB 的中点T 在直线OP 上，且A O B 、、三点不共线． (I)求椭圆的方程及直线AB 的斜率； (Ⅱ)求PAB ?面积的最大值． - 、
专业资料 1. 设抛物线y2 2 px( p 0) 的焦点为F，点 A(0, 2) .若线段FA的中点B在抛物线上， 则 B 到该抛物线准线的距离为_____________ 。（3 分） 2 . 已知m＞1，直线l : x my m20 ，椭圆 C : x 2 y21， F1,F2分别为椭圆C的左、 2m2 右焦点 . （Ⅰ）当直线l过右焦点 F2时，求直线l的方程；（Ⅱ）设直线 l 与椭圆 C 交于A, B两点，V AF1F2，V BF1F2的重心分别为G, H .若原点O在以线段GH为直径的圆内，求实数m 的取值范围. （6 分） 3 已知以原点 O为中心，F5,0 为右焦点的双曲线 C 的离心率e 5 。2 （I）求双曲线C的标准方程及其渐近线方程；（I I ）如题（20）图，已知过点M x1, y1 的直线 l1 : x1 x 4 y1 y 4 与过点 N x2 , y2（其中 x2x ）的直 线 l2 : x2 x 4 y2 y 4 的交点E在 双曲线 C 上，直线MN与两条渐近 线分别交与G、H两点，求OGH 的面积。（8 分）
4. 如图，已知椭圆x2y21(a＞ b＞0) 的离心率为2 ，以该椭圆上的点和椭圆的左、右 a2b22 焦点 F1 , F2为顶点的三角形的周长为4( 2 1) .一等轴双曲线的顶点是该椭圆的焦点，设 P 为该双曲线上异于顶点的任一点，直线PF1和 PF2与椭圆的交点分别为A、B和C、D. （Ⅰ）求椭圆和双曲线的标准方程；（Ⅱ）设直线PF1、 PF2的斜率分别为 k1、 k2，证明 k1·k2 1 ；（Ⅲ）是否存在常数，使得 A B C D A·B C恒D成立？若存在，求的值；若不存在，请说明理由. （ 7 分） 5. 在平面直角坐标系 x2y2 xoy 中，如图，已知椭圆1