解题方法
1 . 已知
,
分别为椭圆C:
的左、右焦点,离心率
,点E在椭圆C上,
的面积的最大值为
.
(1)求C的方程;
(2)设C的上、下顶点分别为A,B,点M是C上异于A,B的任意一点,直线MA,MB分别与x轴交于P,Q两点,O为坐标原点,证明:
为定值.
![](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/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c7316976a221c051a2c14df80b1347.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a44bdca9acbb1daba93f5373298a2567.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
(1)求C的方程;
(2)设C的上、下顶点分别为A,B,点M是C上异于A,B的任意一点,直线MA,MB分别与x轴交于P,Q两点,O为坐标原点,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bab77b1212086d7b16e288f73a09560.png)
您最近一年使用:0次
2023-03-23更新
|
416次组卷
|
3卷引用:四川省南充市嘉陵第一中学2022-2023学年高二下学期6月月考数学(理科)试题
名校
解题方法
2 . 在圆
上任取一点P,过点P作y轴的垂线,垂足为D,点Q满足
.当点P在圆O上运动时,点Q的轨迹为曲线C.
(1)求曲线C的方程;
(2)设曲线C与y轴正半轴交点为A,不过点A的直线l与曲线C交于M,N两点,若
,试探究直线l是否过定点.若过定点,求出该点的坐标;若不过定点,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/560adea7b0d4fbe4131fc41f3fcbd871.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a23aafcfd447358932947c36fc0c4c6.png)
(1)求曲线C的方程;
(2)设曲线C与y轴正半轴交点为A,不过点A的直线l与曲线C交于M,N两点,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32476e6bf0fed9c3d3f23ebfd40aa693.png)
您最近一年使用:0次
2023-03-21更新
|
531次组卷
|
6卷引用:四川省德阳市第五中学2022-2023学年高二下学期4月月考数学(文)试题
四川省德阳市第五中学2022-2023学年高二下学期4月月考数学(文)试题四川省德阳市第五中学2022-2023学年高二下学期4月月考数学(理)试题贵州省毕节市2023届高三诊断性考试(二)数学(文)试题贵州省毕节市2023届高三诊断性考试(二)数学(理)试题(已下线)专题15解析几何(解答题)(已下线)专题15解析几何(解答题)
解题方法
3 . 已知椭圆
,四点
,
,
,
中恰有三点在C上.
(1)求C的方程;
(2)若圆
的切线l与C交于点A,B,证明
为定值,并求出定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc5c0c09aa35241a472f08d94909a82b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fcdfcac1c0075d5ea3a12632aecf670.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c535abcc5765c21dd5975061390484da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/651534f1967f00179cf1ecc59a7cae10.png)
(1)求C的方程;
(2)若圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03e6bedb066ee81c299629cccf35f186.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5b16340e2a6df3b857b3456a903e9c4.png)
您最近一年使用:0次
2023-03-16更新
|
413次组卷
|
3卷引用:四川省南充市嘉陵第一中学2022-2023学年高二下学期第一次月考理科数学试题
四川省南充市嘉陵第一中学2022-2023学年高二下学期第一次月考理科数学试题湖北省襄阳市部分学校2022-2023学年高二下学期3月联考数学试题(已下线)高二数学下学期期中模拟试题02(数列、导数、计数原理)-【同步题型讲义】2022-2023学年高二数学同步教学题型讲义(人教A版2019选修)
4 . 已知椭圆
的左、右焦点分别为
,
,左顶点为
,离心率为
,经过
的直线交椭圆于
两点,
的周长为8.
(1)求椭圆
的方程;
(2)过直线
上一点P作椭圆C的两条切线,切点分别为
,
①证明:直线
过定点;
②求
的最大值.
备注:若点
在椭圆C:
上,则椭圆C在点
处的切线方程为
.
![](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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8376a8a3dd42eaa0558501a3e2a2bdb4.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
①证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b39b4ab8209e56bf6ece460b90c3f1b9.png)
备注:若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23b4f86e48e2b0d63c1865c60ed1e4d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23b4f86e48e2b0d63c1865c60ed1e4d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a9656735f55e5de465e5667ba578d4e.png)
您最近一年使用:0次
解题方法
5 . 在平面内动点P与两定点
连线斜率之积为
.
(1)求动点P的轨迹E的方程;
(2)已知点
,过点P作轨迹E的切线其斜率记为
,当直线
斜率存在时分别记为
.探索
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/e2617c69c6a620278a1b11f1094a9d54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/459c84c9addfbd1cdd0a877ba7c584e4.png)
(1)求动点P的轨迹E的方程;
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f49644cd9fa4688cc3a74a234952530.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bcb166b53a49e393871bcb14a528792.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25d82387e48eafb286785a21a8d4150f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d837dd33cfc22e5414ec57a358a8184.png)
您最近一年使用:0次
解题方法
6 . 已知椭圆
左右焦点分别为
,上顶点为C,
,过点
作
的垂线与椭圆E交于A,B两点,
的周长为8.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/17/ca63c35c-4866-4502-880d-1b047af21cb0.png?resizew=171)
(1)求椭圆E的标准方程;
(2)已知点
为椭圆E上一动点,过点P作E的切线其斜率记为k,当直线
斜率存在时分别记为
,探索
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/e7e5578ca83f5bd5c285994061b9c015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac6a68e28022a8cc17cdc78d5098a950.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c738d79a58541893b80507871c348f66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/17/ca63c35c-4866-4502-880d-1b047af21cb0.png?resizew=171)
(1)求椭圆E的标准方程;
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65e7a27d1917ec235943f4d5116a4160.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25d82387e48eafb286785a21a8d4150f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d837dd33cfc22e5414ec57a358a8184.png)
您最近一年使用:0次
名校
解题方法
7 . 已知椭圆
过点
,且焦距为
.
(1)求椭圆
的方程;
(2)过直线
(不经过点
交椭圆
于点
,
,试问直线
与直线
的斜率之和为
,求证:
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a18deb8273ee656d1261766b469ee2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b10e8abf8690e4b129466ddb918bcc94.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a252d8c461cf65a0b831690cd431307f.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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2023-03-16更新
|
484次组卷
|
2卷引用:四川省凉山州宁南中学2022-2023学年高二下学期第一次月考理科数学试题
8 . 已知过点
的椭圆
:
的焦距为2,其中
为椭圆
的离心率.
(1)求
的标准方程;
(2)设
为坐标原点,直线
与
交于
两点,以
,
为邻边作平行四边形
,且点
恰好在
上,试问:平行四边形
的面积是否为定值?若是定值,求出此定值;若不是,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e93c13c9d1a1f85ab7a9b044c669bf53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/098a3e7d1f1890863b7483a98b618119.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828628c0876b45381c9a0edeb0fec236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3241d7fedd89d85711acd7a2635298af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3241d7fedd89d85711acd7a2635298af.png)
您最近一年使用:0次
2023-03-14更新
|
1945次组卷
|
10卷引用:四川省宜宾市叙州区第二中学校2022-2023学年高二下学期3月月考数学(理)试题
四川省宜宾市叙州区第二中学校2022-2023学年高二下学期3月月考数学(理)试题云南省昆明市2023届“三诊一模”高三复习教学质量检测数学陕西省汉中市2023届高三下学期第二次教学质量检测理科数学试题湖北省武汉市武钢三中2022-2023学年高二下学期3月月考数学试题(已下线)专题16圆锥曲线(解答题)河南省南阳市第一中学校2022-2023学年下期高二第四次月考数学试题宁夏吴忠市吴忠中学2022-2023学年高二下学期期末考试数学(理)试题(已下线)选择性必修一 综合测试-2023-2024学年高二数学同步精品课堂(人教B版2019选择性必修第一册)2024届高三高考模拟综合测试数学试题(一)(已下线)专题15 圆锥曲线综合
9 . 已知椭圆
的离心率为
,以C的短轴为直径的圆与直线
相切.
(1)求C的方程;
(2)直线
:
与C相交于A,B两点,过C上的点P作x轴的平行线交线段AB于点Q,直线OP的斜率为
(O为坐标原点),△APQ的面积为
.
的面积为
,若
,判断
是否为定值?并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8591c458c5675e87f9f9f8ac2b710ea9.png)
(1)求C的方程;
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73e98e989c0f10700ea51b2c6a8efc12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7e08d5c04f0431fb57b33a01717b599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8dcc9f79fe5f07f25447aa442ee14ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0832f7f02ec077d4a0061bc5f67c6722.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/612367da04a206b8b4369985c367e8f2.png)
您最近一年使用:0次
2023-03-14更新
|
3928次组卷
|
5卷引用:四川省成都市简阳市阳安中学2023届高考适应性考试数学(理科)试题
解题方法
10 . 已知椭圆
的长轴长为
,离心率为
,
为
上的两个动点,且直线
与
斜率之积为
(
为坐标原点),则椭圆
的短轴长为_______ ,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27182441bf8c240f102ce7a481642f01.png)
_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f0009063fe00277645aff1be6e32471.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/602baac86c2b1668ecdfadc8a5948885.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27182441bf8c240f102ce7a481642f01.png)
您最近一年使用:0次
2023-03-14更新
|
879次组卷
|
3卷引用:四川省成都市简阳市阳安中学2023届高三下学期三诊模拟考试数学(文科)试题