名校
解题方法
1 . 已知椭圆
的短轴长为2,点
,
分别是椭圆
的左、右焦点,点
为椭圆
的上顶点,直线
的斜率为
.
(1)求椭圆
的方程;
(2)不过右焦点
的直线
与以短轴为直径的圆相切,且与椭圆
交于
两点,直线
与
轴交点记为
.
(ⅰ)若
,证明:
为定值;
(ⅱ)若
,求
周长的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/cabea664e61863b3b3279dbce607924e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827ccf0c04aa941ba20d5f4c6068b46b.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)不过右焦点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c548ef5ad86b7a300495982830f26303.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f44755c5fee4b90266eac73ad47a128.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/439e95540157803d4ac3cf61a49f50a8.png)
(ⅰ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fff6e7e2b9f2b68b1647f6350b98dc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9432da266381b86fa72f507becc4ac3f.png)
(ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aeae227ddcd963101c96448b12a69d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4b5c81ee16e93e9822c4dc54c362cb3.png)
您最近一年使用:0次
2 . 已知椭圆
.
(1)若点
在椭圆C上,证明:直线
与椭圆C相切;
(2)设曲线
的切线l与椭圆C交于
两点,且以
为切点的椭圆C的切线交于M点,求
面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb4402aeb853b22f20992156957ef0fd.png)
(1)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7775aa57ca0e62216f3039ed88dceed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b7b5a74a10686910113e756e5add888.png)
(2)设曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b88b568e07e21bc32b1ba505d91b2083.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a11cb104b04c4e6a1be700e81da279a.png)
您最近一年使用:0次
3 . 已知椭圆
的左、右焦点分别为
,直线
与
交于
两点,
为
上异于
的点.设直线
的斜率分别为
.
(1)若三角形
的面积为2,求点
的坐标;
(2)若
,证明:直线
过定点;
(3)若
,求
满足的关系式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72d7c5f032173b0bc1bb1f197320a539.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fc5bd66dd6d5e09ff0893a938aed56e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790ef3382b1c731f2885eecfd92c2a86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
(1)若三角形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd5a8e1bc9748e5519dcd9981b7eb251.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe726f62de034009c1a4e31e7da04a1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b5536853a7125ff8a7bf913299a2425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee956329e95a172d86c86b2f6af7aec.png)
您最近一年使用:0次
名校
解题方法
4 . 已知椭圆
的离心率为
,直线
截椭圆
所得的弦长为
.
(1)求椭圆
的标准方程;
(2)设直线
与
轴交于点
为粗圆
上的两个动点、且均位于第一象限(不在直线
上),直线
、
分别交椭圆于
两点,直线
分别交直线
于
两点.
①设
,试用
表示
的坐标;
②求证:
为线段
的中点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0c118b51ab426bc1c1b56179094f146.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbc2dfda09549eac62c6f0c47d70625a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a253c7fdf589ee3dece13d5b5b5732.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8f90eb172dbd2ff7ae6f705801c0737.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ba48366317ebea1c9dd5e4e67e03092.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cf9b288c48c73463a2f214f02b6952a.png)
①设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c663466d641b5fdfef1e529d6c330ecf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eaf2102b730fe50c8681f1a6fafe67af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/166afeb61d5a80366a8ae29c912cd644.png)
②求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
您最近一年使用:0次
2024·全国·模拟预测
名校
解题方法
5 . 已知直线
和椭圆
.
(1)证明:
与
恒有两个交点;
(2)若
为
与
的两个交点,过原点且垂直于
的直线交
于
两点,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b648c913b1b66abb9cd526dd8a7b2ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0b0ae6048bf94ccd5a3b4a8aafd81e.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ce9db8bf6dff7b5b1feb849f5532f22.png)
您最近一年使用:0次
名校
解题方法
6 . 如图,已知椭圆
经过点
,离心率
.
的标准方程;
(2)椭圆
上任意点
轴上一点
,若
的最小值为
,求实数
的取值范围;
(3)设
是经过右焦点
的任一弦(不经过点
),直线
与直线
相交于点
,记
的斜率分别为
,求证:
成等差数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04147e15b00989da8277da4422f8b443.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c7316976a221c051a2c14df80b1347.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81828dcd00a71cf376e8003488886bb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4f959ea4e8be882517c570b7bd7ad0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fce0dbfbaede9bcbc415a105e36688e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43c58b986bea8854118adc80af4437ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/495bb3e5a3a9d35f5c9f0cf1f5d51876.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/166a8e1bcb93423697696e2ba0409fbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dca1726d463bd741c904abd9b6589056.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbf3a71536f4f45cd75732e8b48592eb.png)
您最近一年使用:0次
2024-03-29更新
|
469次组卷
|
4卷引用:上海市松江二中2023-2024学年高二下学期期中数学试卷
上海市松江二中2023-2024学年高二下学期期中数学试卷上海市向明中学2023-2024学年高二下学期3月月考数学试题湖北省武汉市第二中学2023-2024学年高三下学期模拟考试(最后一卷)数学试卷(已下线)专题02圆锥曲线全章复习攻略--高二期末考点大串讲(沪教版2020选修一)
名校
解题方法
7 . 已知椭圆C:
过点
,长轴长为
.
(1)求椭圆方程及离心率;
(2)直线l:
与椭圆C交于两点M、N,直线AM、AN分别与直线
交于点P、Q,O为坐标原点且
,求证:直线l过定点,并求出定点坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfaba0309c471a4246ca3254a3cdaf17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e2031d209711b058f3d278ede3c1d33.png)
(1)求椭圆方程及离心率;
(2)直线l:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15b256345d7109e081b7c895591e995d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a089c207e39a24d0d82aa853ac2bbb8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/030c0325fde242e06cee8d270ba89d68.png)
您最近一年使用:0次
2024-03-06更新
|
931次组卷
|
4卷引用:福建省厦门第一中学2023-2024学年高二下学期期中考试数学试卷
8 . 设椭圆
,
,
分别是C的左、右焦点,C上的点到
的最小距离为1,P是C上一点,且
的周长为6.
(1)求C的方程;
(2)过点
且斜率为k的直线l与C交于M,N两点,过原点且与l平行的直线与C交于A,B两点,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
(1)求C的方程;
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1a3c79973f7fa2547db303c1279277.png)
您最近一年使用:0次
2024-03-24更新
|
209次组卷
|
2卷引用: 四川省什邡中学2023-2024学年高二下学期期中考试数学试题
名校
9 . 如图,由部分椭圆
和部分双曲线
,组成的曲线
称为“盆开线”.曲线
与
轴有
两个交点,且椭圆与双曲线的离心率之积为
.
的直线
与
相切于点
,求部分椭圆方程、部分双曲线方程及直线
的方程;
(2)过
的直线
与
相交于点
三点,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/573d0b25ac3ea513b454e803dc9b67a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1248f0dcc3786ba984dc7fc88cf62e8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/526e16c3287f8195d925b3805e0b3c1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/059d02ae074c7c2f7dfde8058dfa55ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff32d26c8d44f5fb4813a19c1030a9f5.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/762c7b2136f8428ff7ec20fd8efd03c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bf70a4a36f163ceee458c6963b2bee5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29fda29f1b1b042a89c0213f18d341ad.png)
您最近一年使用:0次
名校
解题方法
10 . 在平面直角坐标系xOy中,椭圆
的左焦点为点F,离心率为
,过点F且与x轴垂直的直线被椭圆截得的线段长为3.
(1)求椭圆C的方程;
(2)设不过原点O且斜率为
的直线l与椭圆C交于不同的两点P,Q,线段PQ的中点为T,直线OT与椭圆C交于两点M,N,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(1)求椭圆C的方程;
(2)设不过原点O且斜率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b20553e0b4f149dd34c3623676149d43.png)
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