名校
解题方法
1 . 已知
,
,M是圆O:
上任意一点,
关于点M的对称点为N,线段
的垂直平分线与直线
相交于点T,记点T的轨迹为曲线C.
(1)求曲线C的方程;
(2)设
(
)为曲线C上一点,不与x轴垂直的直线l与曲线C交于G,H两点(异于E点).若直线GE,HE的斜率之积为2,求证:直线l过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/813f9a2814013e2407b5b1c216159359.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16fd15503ee692f8286b0312f7c6f0cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7272356beb98a7953a49651324cb6455.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfbdbe9a17a23c44cec8c7475c4dc1a9.png)
(1)求曲线C的方程;
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d54a59ba55d5e12ae8b643e60a1bb49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fff6e7e2b9f2b68b1647f6350b98dc8.png)
您最近一年使用:0次
2024-05-24更新
|
570次组卷
|
2卷引用:江西省重点中学盟校2024届高三第二次联考数学试题
2024高三下·全国·专题练习
解题方法
2 . 已知点
为椭圆
上任意一点,直线
,点F为椭圆C的左焦点.
(1)求椭圆C的离心率及左焦点F的坐标;
(2)求证:直线与椭圆C相切;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3511cdc6a9b56bc1d9415d3d94ef0f67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/533b93dd6eb6b474481247736699c76c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/482aa1008b1009aa649b2e44a5d05a16.png)
(1)求椭圆C的离心率及左焦点F的坐标;
(2)求证:直线与椭圆C相切;
您最近一年使用:0次
名校
解题方法
3 . 已知椭圆
的右焦点为F,C在点
处的切线l分别交直线
和直线
于
两点.
(1)求证:直线
与C相切;
(2)探究:
是否为定值?若是,求出该定值;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/533b93dd6eb6b474481247736699c76c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/021bcc5ea186cd32c39b3d333b0f448c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
(1)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7b40ab6df8dd73aa89fef3c81df6fb9.png)
(2)探究:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35dc962d118cd70c761f7870b3e59c2d.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
,左右焦点分别为
,
是椭圆上一点,
,
.
(1)求椭圆的方程;
(2)过点
的直线与椭圆交于
两点,
为线段
中点.
(i)求证:
点轨迹方程为
;
(ii)
为坐标原点,射线
与椭圆交于点
,点
为直线
上一动点,且
,求证:点
在定直线上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a74e28144cbed9111d17dd239136f80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6b646abc8ee6b9c8558d898f2af4be1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74404619ad5699e6c44c947fb569600f.png)
(1)求椭圆的方程;
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b0a807a550b61acd46aa4f8677dd6d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
(i)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f62518b67e16e5c04a2d6be20c476fb0.png)
(ii)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84fb85c78522640bcaf889f89ad89de9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84fb85c78522640bcaf889f89ad89de9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a281a22f6ce9def698919a6d1a04c389.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
您最近一年使用:0次
名校
解题方法
5 . 已知椭圆
的左、右焦点分别为
为上顶点,离心率 为
,直线
与圆
相切.
(1)求椭圆
的标准方程;
(2)椭圆方程
,平面上有一点
. 定义直线方程
是椭圆
在点
处的极线.
① 若
在椭圆
上,证明: 椭圆
在点
处的极线就是过点
的切线;
② 若过点
分别作椭圆
的两条切线和一条割线,切点为
,割线交椭圆
于
两点,过点
分别作椭圆
的两条切线,且相交于点
. 证明:
三点共线.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d81afe11925b30336768531ede1c278.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c72dcc2ad9bd83bf683a3c10aebf1c6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3656055f5256cd06e636ea96e9f89c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70993bac22dd8e80a4d151900785a7fb.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)椭圆方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62645f10a184693406c85b90386b43d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7f137ff5fe9fd34a482228e24e9a55b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e74b54fca09a55c3720426e2dc4dfa9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7f137ff5fe9fd34a482228e24e9a55b.png)
① 若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7f137ff5fe9fd34a482228e24e9a55b.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
② 若过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5eebd2e8567f55a4499c51e3c4eed6c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c55c23f1782d16f190469765e02b8c33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6670479a0083dd2dfd5ad55b47b1ab6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6670479a0083dd2dfd5ad55b47b1ab6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f90c72d708d6d7693d4727ae7882317.png)
您最近一年使用:0次
名校
解题方法
6 . 已知椭圆
,设过点
的直线
交椭圆
于M,N两点,交直线
于点
,点
为直线
上不同于点
的任意一点.
的离心率为
,求
的值;
(2)若
,求
的取值范围;
(3)若
,记直线
,
,
的斜率分别为
,
,
,问是否存在
,
,
的某种排列
,
,
(其中
,使得
,
,
成等差数列或等比数列?若存在,写出结论,并加以证明;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e756feec2851b90497421790a7206e76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c6ff81aedbefa935da289dc632e78eb.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/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.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/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a240645e301f75ac5de5ae863f471797.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3c442579603164f3fc19458677d307.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f30cb81835298cb612a828f355060a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d385f60d35804535c78ae45fe4e4501.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af6cd332590b9eb4032b51a39134d219.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbf434334b09cc0fdd4e86e84e6ceb00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbf434334b09cc0fdd4e86e84e6ceb00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8cc03cd251a03b73ebae3ea1d6bca76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be2eb8885dc1f43959efc27d89291c61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b84ad6ffc62173c68ff3ca5cf19f14b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64445096415ca58ef1b9b0fb8e6e24d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8cc03cd251a03b73ebae3ea1d6bca76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be2eb8885dc1f43959efc27d89291c61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b84ad6ffc62173c68ff3ca5cf19f14b9.png)
您最近一年使用:0次
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7 . 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
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解题方法
8 . 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
9 . 已知椭圆
的左、右焦点分别为
为坐标原点,直线
与
交于
两点,点
在第一象限,点
在第四象限且满足直线
与直线
的斜率之积为
.当
垂直于
轴时,
.
(1)求
的方程;
(2)若点
为
的左顶点且满足
,直线
与
交于
,直线
与
交于
.
①证明:
为定值;
②证明:四边形
的面积是
面积的2倍.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3324199c6751f2e0e6d8542783b0d957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d4baaf1a6c7794dc95ba89c9e2820c3.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/01c74a907dda6bb7d9d56d009d9df253.png)
![](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/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/602baac86c2b1668ecdfadc8a5948885.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/24dd2505b79dc4bad657e97c6bfd6c9c.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/742ff39a10a7fc9deb693abb7fe26680.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
①证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02c07b101a1a118c7558a9e59b13c95c.png)
②证明:四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d89641052a363c69069bc2d747eebf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
您最近一年使用:0次
解题方法
10 . 已知椭圆
的离心率为
,且a,b的等比中项为2.
(1)求C的方程;
(2)若直线
与C交于点A,B两点,直线
过点A且与C交于另外一点
,直线
过点B,且与C交于另外一点
.
(ⅰ)设
,
,证明:
;
(ⅱ)若直线
的斜率为
,判断是否存在常数m,使得k是m,
的等比中项,若存在,求出m的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
(1)求C的方程;
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b343d77ee4dced82ecc479206c42977d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58e82f042b992b3c56a7a0ba26033aef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93f427c66fb1e0c7bc55dc741867d9fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3953cec61ac602ce5eb59b7912352179.png)
(ⅰ)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6ff82ebdfad5e7de1c7487b0b817a7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c848021933bfdfc20370d7a188aa356.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcbe0f3e0c41f79c15cbae31aa979065.png)
(ⅱ)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb0628cecbfc98d390e5447d52414e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7e08d5c04f0431fb57b33a01717b599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/110ee60613ccf45d772870bc9297c708.png)
您最近一年使用:0次