名校
1 . 设关于x的方程2x2﹣ax﹣2=0的两根分别为α、β(α<β),函数
(1)证明f(x)在区间(α,β)上是增函数;
(2)当a为何值时,f(x)在区间[α,β]上的最大值与最小值之差最小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/212e78e289a58fae2d81c9abd463f45c.png)
(1)证明f(x)在区间(α,β)上是增函数;
(2)当a为何值时,f(x)在区间[α,β]上的最大值与最小值之差最小.
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2017-10-08更新
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5卷引用:2017届上海市上海中学高考模拟试卷(3)数学试题
2 . 已知椭圆
的右焦点与短轴两端点构成一个面积为2的等腰直角三角形,
为坐标原点.
(1)求椭圆
的方程;
(2)设点
在椭圆
上,点
在直线
上,且
,求证:
为定值;
(3)设点
在椭圆
上运动,
,且点
到直线
的距离为常数
,求动点
的轨迹方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1193fec7c34d581b448525a32e7256e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/506ac99eff77facdc461b1ae4dd8077c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87be53262d72dda5dd55d79ab20ff0b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9d40b60b217146f67847f1489673570.png)
(3)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b6282f1ad5c999c8cee7115da76c18a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ffb98f1e3c1317c0db403d3af04bdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c3f8c3ba00c59e0634ed10fa85289de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
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3卷引用:2016届上海市闵行区高三4月质量调研(二模)(文)数学试题
3 . 设椭圆
的长半轴长为
,短半轴长为
,椭圆
的长半轴长为
,短半轴长为
,若
,则称椭圆
与椭圆
是相似椭圆.已知椭圆
,其左顶点为
,右顶点为
.
(1)设椭圆
与椭圆
是“相似椭圆”,求常数
的值;
(2)设椭圆
,过
作斜率为
的直线
与椭圆
仅有一个公共点,过椭圆
的上顶点
作斜率为
的直线
与椭圆
只有一个公共点,当
为何值时,
取得最小值,试求出最小值;
(3)已知椭圆
与椭圆
是相似椭圆,椭圆
上异于
的任意一点
,求证:
的垂心
在椭圆
上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/522230546d4b802094e86ceb48c2ba38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b715e7842b95f654f16056a7c7f2abe9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b4f150ab98bde511e0f65d9bafab031.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13423c094861baf4b759b7f3d8c3c226.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd731967bb86ddf18e9e473daa96041a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/522230546d4b802094e86ceb48c2ba38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b4f150ab98bde511e0f65d9bafab031.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ff1455a4045eb93f482c0751840aea7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(1)设椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d56cbbfc76e5d203ea5efffbbc6d291.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5873c01192b7d33b7483f444f90b5b0.png)
(2)设椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96d6ba128a26fe49c989ba5f6538e5f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff4489d9b83072184c0e1d6b09be50ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f0b669ef4514f24ee09adeff7f41238.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05d1e1062878dcb155964639267bdedf.png)
(3)已知椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1217c64cc23489dccb61d90a5500da84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b77e6b117cf9d90d7d31d7ebde3dbf5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
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2017-03-03更新
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1165次组卷
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5卷引用:上海市金山中学2016-2017学年高二下学期期末考试数学试题
上海市金山中学2016-2017学年高二下学期期末考试数学试题(已下线)专题5.8 期末考前选做30题(解答题压轴版)-2020-2021学年高二数学下学期期末专项复习(沪教版)2016届上海市浦东新区高三综合练习(三模)数学试题2016-2017学年山东省烟台市高二上学期期末考试数学(理)试卷(已下线)山东省烟台市2016-2017学年高二上学期期末考试理数试题
2013·上海黄浦·二模
名校
解题方法
4 . 设抛物线
的焦点为
,经过点
的动直线
交抛物线
于点
且
.
(1)求抛物线的方程;
(2)若
为坐标原点),且点
在抛物线
上,求直线
斜率;
(3)若点M是抛物线
的准线上的一点,直线MF,MA,MB斜率分别为
.求证:当
为定值时,
也为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4daf40bad1cc89311930cce356672354.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65d335e66dec30244e3ee1c0d193335e.png)
(1)求抛物线的方程;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ce469a735f963e325a76e79d1d3db88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(3)若点M是抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/388737b5d38e8aa7bc8cfb1da4f9fc69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed1e9cdd5a82f29ec89b2c53b4fa6f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b69e3f7ddd51215d00661c09cd900d60.png)
您最近一年使用:0次
5 . 已知椭圆
(
)的左、右焦点分别为
、
,点![](https://img.xkw.com/dksih/QBM/2015/5/13/1572106333437952/1572106339532800/STEM/3cc290616f6f4942ac59da6640358fde.png?resizew=16)
,过点
且与
垂直的直线交
轴负半轴于点
,且
.
(1)求证:△
是等边三角形;
(2)若过
、
、
三点的圆恰好与直线
:
相切,求椭圆
的方程;
(3)设过(2)中椭圆
的右焦点
且不与坐标轴垂直的直线
与
交于
、
两点,
是点
关于
轴的对称点.在
轴上是否存在一个定点
,使得
、
、
三点共线,若存在,求出点
的坐标;若不存在,请说明理由.
![](https://img.xkw.com/dksih/QBM/2015/5/13/1572106333437952/1572106339532800/STEM/a4885230d6c64c71a13826aed84bcc30.png?resizew=99)
![](https://img.xkw.com/dksih/QBM/2015/5/13/1572106333437952/1572106339532800/STEM/90d4ef9e16f641deb2a2782a99a5c854.png?resizew=61)
![](https://img.xkw.com/dksih/QBM/2015/5/13/1572106333437952/1572106339532800/STEM/989529bbf9c940e18fe5523ae8f25a50.png?resizew=17)
![](https://img.xkw.com/dksih/QBM/2015/5/13/1572106333437952/1572106339532800/STEM/c94552212a274a5094fa8d0efda0306b.png?resizew=19)
![](https://img.xkw.com/dksih/QBM/2015/5/13/1572106333437952/1572106339532800/STEM/3cc290616f6f4942ac59da6640358fde.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2015/5/13/1572106333437952/1572106339532800/STEM/0ea4527f5d3b42d0956dd13c5fbfffc9.png?resizew=43)
![](https://img.xkw.com/dksih/QBM/2015/5/13/1572106333437952/1572106339532800/STEM/3cc290616f6f4942ac59da6640358fde.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2015/5/13/1572106333437952/1572106339532800/STEM/dfa755297bd44c8092ac135f648db551.png?resizew=29)
![](https://img.xkw.com/dksih/QBM/2015/5/13/1572106333437952/1572106339532800/STEM/6732036432a547f5b1b58e92176d8e9d.png?resizew=13)
![](https://img.xkw.com/dksih/QBM/2015/5/13/1572106333437952/1572106339532800/STEM/1f4dbca7ecba4c919440f19c728db468.png?resizew=17)
![](https://img.xkw.com/dksih/QBM/2015/5/13/1572106333437952/1572106339532800/STEM/c30908dc1fbe4192b058abfa0673fc5f.png?resizew=109)
(1)求证:△
![](https://img.xkw.com/dksih/QBM/2015/5/13/1572106333437952/1572106339532800/STEM/ae93578723f24a0b9059d57d5cc60e8c.png?resizew=41)
(2)若过
![](https://img.xkw.com/dksih/QBM/2015/5/13/1572106333437952/1572106339532800/STEM/3cc290616f6f4942ac59da6640358fde.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2015/5/13/1572106333437952/1572106339532800/STEM/1f4dbca7ecba4c919440f19c728db468.png?resizew=17)
![](https://img.xkw.com/dksih/QBM/2015/5/13/1572106333437952/1572106339532800/STEM/c94552212a274a5094fa8d0efda0306b.png?resizew=19)
![](https://img.xkw.com/dksih/QBM/2015/5/13/1572106333437952/1572106339532800/STEM/cba65ef8b6024d398ceab07fb83bb342.png?resizew=9)
![](https://img.xkw.com/dksih/QBM/2015/5/13/1572106333437952/1572106339532800/STEM/3de06a8c064c487cb2096b2aba439344.png?resizew=101)
![](https://img.xkw.com/dksih/QBM/2015/5/13/1572106333437952/1572106339532800/STEM/976bd0f2091a470bb3059df6211f87f5.png?resizew=16)
(3)设过(2)中椭圆
![](https://img.xkw.com/dksih/QBM/2015/5/13/1572106333437952/1572106339532800/STEM/976bd0f2091a470bb3059df6211f87f5.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2015/5/13/1572106333437952/1572106339532800/STEM/c94552212a274a5094fa8d0efda0306b.png?resizew=19)
![](https://img.xkw.com/dksih/QBM/2015/5/13/1572106333437952/1572106339532800/STEM/cba65ef8b6024d398ceab07fb83bb342.png?resizew=9)
![](https://img.xkw.com/dksih/QBM/2015/5/13/1572106333437952/1572106339532800/STEM/976bd0f2091a470bb3059df6211f87f5.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2015/5/13/1572106333437952/1572106339532800/STEM/c5738965810e49a68b0bf33605d311f6.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2015/5/13/1572106333437952/1572106339532800/STEM/443824ad89914928886d3d2cada25db4.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2015/5/13/1572106333437952/1572106339532800/STEM/e1f42eedf951449da2f947d01522f8be.png?resizew=21)
![](https://img.xkw.com/dksih/QBM/2015/5/13/1572106333437952/1572106339532800/STEM/c5738965810e49a68b0bf33605d311f6.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2015/5/13/1572106333437952/1572106339532800/STEM/6732036432a547f5b1b58e92176d8e9d.png?resizew=13)
![](https://img.xkw.com/dksih/QBM/2015/5/13/1572106333437952/1572106339532800/STEM/6732036432a547f5b1b58e92176d8e9d.png?resizew=13)
![](https://img.xkw.com/dksih/QBM/2015/5/13/1572106333437952/1572106339532800/STEM/29b12f61755a4c7299b9016e553aacd2.png?resizew=19)
![](https://img.xkw.com/dksih/QBM/2015/5/13/1572106333437952/1572106339532800/STEM/e1f42eedf951449da2f947d01522f8be.png?resizew=21)
![](https://img.xkw.com/dksih/QBM/2015/5/13/1572106333437952/1572106339532800/STEM/443824ad89914928886d3d2cada25db4.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2015/5/13/1572106333437952/1572106339532800/STEM/29b12f61755a4c7299b9016e553aacd2.png?resizew=19)
![](https://img.xkw.com/dksih/QBM/2015/5/13/1572106333437952/1572106339532800/STEM/29b12f61755a4c7299b9016e553aacd2.png?resizew=19)
您最近一年使用:0次
2014·上海·一模
6 . 在平面直角坐标系
中,原点为
,抛物线
的方程为
,线段
是抛物线
的一条动弦.
(1)求抛物线
的准线方程和焦点坐标
;
(2)若
,求证:直线
恒过定点;
(3)当
时,设圆
,若存在且仅存在两条动弦
,满足直线
与圆
相切,求半径
的取值范围?
![](https://img.xkw.com/dksih/QBM/2014/6/3/1571751315103744/1571751320526848/STEM/cdc1f382acc54499a528acf682af6da7.png?resizew=32)
![](https://img.xkw.com/dksih/QBM/2014/6/3/1571751315103744/1571751320526848/STEM/5c8c8bfbd66d49adae210d3697268718.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2014/6/3/1571751315103744/1571751320526848/STEM/3a710560070749748cea135b10864e4c.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2014/6/3/1571751315103744/1571751320526848/STEM/17bd47777ce3471483caff4135969379.png?resizew=53)
![](https://img.xkw.com/dksih/QBM/2014/6/3/1571751315103744/1571751320526848/STEM/9e9a4160068e4715891c6168059aa284.png?resizew=27)
![](https://img.xkw.com/dksih/QBM/2014/6/3/1571751315103744/1571751320526848/STEM/3a710560070749748cea135b10864e4c.png?resizew=16)
(1)求抛物线
![](https://img.xkw.com/dksih/QBM/2014/6/3/1571751315103744/1571751320526848/STEM/3a710560070749748cea135b10864e4c.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2014/6/3/1571751315103744/1571751320526848/STEM/766fff83756e4e808c2413698264f4ce.png?resizew=17)
(2)若
![](https://img.xkw.com/dksih/QBM/2014/6/3/1571751315103744/1571751320526848/STEM/b06be35bff69499d91eda06d10c97e1e.png?resizew=89)
![](https://img.xkw.com/dksih/QBM/2014/6/3/1571751315103744/1571751320526848/STEM/9e9a4160068e4715891c6168059aa284.png?resizew=27)
(3)当
![](https://img.xkw.com/dksih/QBM/2014/6/3/1571751315103744/1571751320526848/STEM/a06d26a8d2ec4784b8cfea98b0eb3ca0.png?resizew=53)
![](https://img.xkw.com/dksih/QBM/2014/6/3/1571751315103744/1571751320526848/STEM/a3b4f1c64f7040c485a9a71ce65cf5be.png?resizew=179)
![](https://img.xkw.com/dksih/QBM/2014/6/3/1571751315103744/1571751320526848/STEM/9e9a4160068e4715891c6168059aa284.png?resizew=27)
![](https://img.xkw.com/dksih/QBM/2014/6/3/1571751315103744/1571751320526848/STEM/9e9a4160068e4715891c6168059aa284.png?resizew=27)
![](https://img.xkw.com/dksih/QBM/2014/6/3/1571751315103744/1571751320526848/STEM/8188c4a6b1cf4f9395aadb911ec2665c.png?resizew=17)
![](https://img.xkw.com/dksih/QBM/2014/6/3/1571751315103744/1571751320526848/STEM/fb8ef1baabf247ffac5addecd516b201.png?resizew=12)
您最近一年使用:0次
7 . 设圆
的圆心为A,直线l过点B(1,0)且与x轴不重合,l交圆A于C,D两点,过B作AC的平行线交AD于点E.
(I)证明
为定值,并写出点E的轨迹方程;
(II)设点E的轨迹为曲线C1,直线l交C1于M,N两点,过B且与l垂直的直线与圆A交于P,Q两点,求四边形MPNQ面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/714df7f0c804617e1c8832d2e91b496a.png)
(I)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13b2b09f9c6800d238e8d34018a01fb1.png)
(II)设点E的轨迹为曲线C1,直线l交C1于M,N两点,过B且与l垂直的直线与圆A交于P,Q两点,求四边形MPNQ面积的取值范围.
您最近一年使用:0次
2016-12-04更新
|
10679次组卷
|
46卷引用:《高频考点解密》—解密18 圆与方程
(已下线)《高频考点解密》—解密18 圆与方程上海实验学校2022届高三冲刺模拟4数学试题2016年全国普通高等学校招生统一考试理科数学(新课标1卷精编版)(已下线)二轮复习 【理】专题16 圆锥曲线的综合应用 押题专练(已下线)二轮复习【文】专题15 圆锥曲线的综合应用 押题专练(已下线)《考前20天终极攻略》5月28日 圆锥曲线【理科】(已下线)《考前20天终极攻略》5月28日 圆锥曲线【理科】(已下线)《高频考点解密》—解密19 椭圆(已下线)《高频考点解密》—解密23 曲线与方程2018年春高考数学(理)二轮专题复习训练:专题四 解析几何、坐标系与参数方程智能测评与辅导[理]-圆锥曲线的综合应用广西壮族自治区南宁市宾阳县宾阳中学2019-2020学年高二上学期9月月考数学(文)试题(已下线)6.1 直线与直线 直线与圆的位置关系与性质[文] -《备战2020年高考精选考点专项突破题集》重庆市朝阳中学2019-2020学年高二上学期12月月考数学试题(已下线)专题9.8 曲线与方程(练)【理】-《2020年高考一轮复习讲练测》专题6.1 直线与直线 直线与圆的位置关系与性质[理]-《备战2020年高考精选考点专项突破题集》安徽省合肥市第六中学2018-2019学年高二下学期开学考试数学试题河南省平顶山市第一中学2019-2020学年高二下学期开学考试数学(理)试题西藏自治区拉萨市拉萨中学2021届高三第一次月考数学(文)试题西藏自治区拉萨市拉萨中学2021届高三第一次月考数学(理)试题(已下线)专题19+选修1-1综合练习-2020-2021学年【补习教材·寒假作业】高二数学(文)(人教A版)(已下线)专题18+选修2-1综合练习-2020-2021学年【补习教材·寒假作业】高二数学(理)(人教A版)(已下线)专题08+选择性必修第一册综合练习-2020-2021学年【补习教材·寒假作业】高二数学(人教A版2019)(已下线)专题9.9 解析几何单元检测-2021年高考数学(文)一轮复习讲练测(已下线)考点30 直线与圆锥曲线-2021年新高考数学一轮复习考点扫描(已下线)综合练习模拟卷05-2021年高考一轮数学(理)单元复习一遍过(已下线)综合练习模拟卷05-2021年高考一轮数学单元复习一遍过(新高考地区专用)(已下线)综合练习模拟卷05-2021年高考一轮数学(文)单元复习一遍过四川省成都市成华区成都市第四十九中学校2019-2020学年高二上学期期中数学试题新高考2021届高三考前保温热身模拟卷数学试题(二)(已下线)专题42 盘点圆锥曲线中的面积问题——备战2022年高考数学二轮复习常考点专题突破(已下线)专题19 圆锥曲线解答题(已下线)专题13 极坐标秒解圆锥曲线 微点1 极坐标秒解圆锥曲线(已下线)专题26 求动点轨迹方程 微点2 定义法求动点的轨迹方程(已下线)专题23 圆锥曲线中的最值、范围问题 微点2 圆锥曲线中的范围问题福建师范大学附属中学2021-2022学年高二上学期期末考试数学试题(已下线)考向37 圆锥曲线中的范围、最值问题(重点)(已下线)11.4 直线与圆锥曲线的位置关系(已下线)专题19 选修1-1综合练习(已下线)专题18 选修2-1综合练习沪教版(2020) 25天高考冲刺 双新双基百分百3(已下线)2016年全国普通高等学校招生统一考试理科数学(全国1卷参考版)四川省阆中中学校2023届高三第五次检测(二模)数学(文)试题广东省潮州市2024届高三上学期期末数学试题(已下线)专题24 解析几何解答题(理科)-1专题36平面解析几何解答题(第一部分)
名校
8 . 如图,椭圆
,
轴被曲线
截得的线段长等于C1的长半轴长.
![](https://img.xkw.com/dksih/QBM/2016/4/12/1572592293142528/1572592299220992/STEM/c8564064-1151-4353-836b-a5bf2d2cfe35.png)
(1)求实数b的值;
(2)设C2与
轴的交点为M,过坐标原点O的直线
与C2相交于点A、B,直线MA、MB分别与C1交于点D、E.
①证明:
;
②记△MAB,△MDE的面积分别是
若
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a9241771f8fd618359504599d75a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6e671afd184e7bb84266ab42357ebbe.png)
![](https://img.xkw.com/dksih/QBM/2016/4/12/1572592293142528/1572592299220992/STEM/c8564064-1151-4353-836b-a5bf2d2cfe35.png)
(1)求实数b的值;
(2)设C2与
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
①证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/443b7f8dbbd43325ded00ce35f521475.png)
②记△MAB,△MDE的面积分别是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0386ef30475321ff3d7d4364accf3fb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a06f26807c92be14f6f2de6ea81d3c2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
2016-12-04更新
|
1353次组卷
|
3卷引用:2016届上海市高境第一中学高三下学期5月热身(理)数学试题
2014·上海虹口·二模
名校
9 . 如图,直线
与抛物线
(常数
)相交于不同的两点
、
,且
(
为定值),线段
的中点为
,与直线
平行的切线的切点为
(不与抛物线对称轴平行或重合且与抛物线只有一个公共点的直线称为抛物线的切线,这个公共点为切点).
![](https://img.xkw.com/dksih/QBM/2014/4/28/1571689046212608/1571689052381184/STEM/8f7e7bc0d83844f8b2973031282baaaa.png)
(1)用
、
表示出
点、
点的坐标,并证明
垂直于
轴;
(2)求
的面积,证明
的面积与
、
无关,只与
有关;
(3)小张所在的兴趣小组完成上面两个小题后,小张连
、
,再作与
、
平行的切线,切点分别为
、
,小张马上写出了
、
的面积,由此小张求出了直线
与抛物线围成的面积,你认为小张能做到吗?请你说出理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f24e616b5a35ff372c78c1472f156ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b35f0b940c8422ef47edc3b7ce55e47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0aa23696b63c7d2d2950980a2c8cdb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9a6bdff3abb2c2d390afd0b8c583361.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff2614099c6c251a50617dc7c17e0ad1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a62c0aeef65f78446c8e0edb0376c89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eabd5f3a86afe49dcd70571e2b96cfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4147cb6273143ff729d220b60a9894e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://img.xkw.com/dksih/QBM/2014/4/28/1571689046212608/1571689052381184/STEM/8f7e7bc0d83844f8b2973031282baaaa.png)
(1)用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/557b46343f25d63ec71d84f34e617c50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/557b46343f25d63ec71d84f34e617c50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eabd5f3a86afe49dcd70571e2b96cfd.png)
(3)小张所在的兴趣小组完成上面两个小题后,小张连
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9bceffe868945d670c0b7f012a4c78b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af7d1945c54a5b5e94b67fcff1df64e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2016-12-02更新
|
1440次组卷
|
3卷引用:2014届上海市虹口区高三4月高考练习(二模)理科数学试卷
11-12高三上·浙江嘉兴·阶段练习
名校
10 . 已知抛物线
的顶点在原点,焦点在
轴正半轴上,点
到其准线的距离等于
.
(Ⅰ)求抛物线
的方程;
(Ⅱ)如图,过抛物线
的焦点的直线从左到右依次与抛物线
及圆
交于
、
、
、
四点,试证明
为定值.
![](https://img.xkw.com/dksih/QBM/2011/11/9/1570346597523456/1570346603012096/STEM/f35dc38c08354d48926a00e9f905751b.png?resizew=201)
(Ⅲ)过
、
分别作抛物
的切线
、
,且
、
交于点
,求
与
面积之和的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59c0980761f2c189bb51b9c12a79d77d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
(Ⅰ)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
(Ⅱ)如图,过抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e318cefab1d71238b6a770e9d5fe154e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ba9fc9ae9bc7000a7f3daba16091a02.png)
![](https://img.xkw.com/dksih/QBM/2011/11/9/1570346597523456/1570346603012096/STEM/f35dc38c08354d48926a00e9f905751b.png?resizew=201)
(Ⅲ)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0288f5a9e234c0fc858c89f0a30c003b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd2640a7425ddd37334d14a5443479b3.png)
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