解题方法
1 . 已知O为坐标系原点,椭圆
的右焦点为点F,右准线为直线n.
(1)过点
的直线交椭圆C于
两个不同点,且以线段
为直径的圆经过原点O,求该直线的方程;
(2)已知直线l上有且只有一个点到F的距离与到直线n的距离之比为
.直线l与直线n交于点N,过F作x轴的垂线,交直线l于点M.求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89ecad87737153d4773746f88d508075.png)
(1)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8e32f16d75ccb62a04970f861827fca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e1e4115d78e625e9e0f47cdade3286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
(2)已知直线l上有且只有一个点到F的距离与到直线n的距离之比为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc7ff4c8dc73f97611be4a9eda1602e7.png)
您最近一年使用:0次
2020高三·全国·专题练习
名校
解题方法
2 . 给定椭圆C:
(a>b>0),称圆心在原点O,半径为
的圆为椭圆C的“准圆”.若椭圆C的一个焦点为F(
,0),其短轴上的一个端点到F的距离为
.
(1)求椭圆C的方程和其“准圆”方程;
(2)若点P是椭圆C的“准圆”上的动点,过点P作椭圆的切线l1,l2交“准圆”于点M,N.证明:l1⊥l2,且线段MN的长为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da001dad7941e6c9858637d7b62cec59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
(1)求椭圆C的方程和其“准圆”方程;
(2)若点P是椭圆C的“准圆”上的动点,过点P作椭圆的切线l1,l2交“准圆”于点M,N.证明:l1⊥l2,且线段MN的长为定值.
您最近一年使用:0次
3 . 已知椭圆Γ:
的右焦点坐标为
,且长轴长为短轴长的
倍,直线l交Γ椭圆于不同的两点
和
,
![](https://img.xkw.com/dksih/QBM/2020/12/24/2621114416979968/2623385264226304/STEM/8dcd37f5f04b48a4af764c5640e9e312.png?resizew=189)
(1)求椭圆Γ的方程;
(2)若直线l经过点
,且
的面积为
,求直线l的方程;
(3)若直线l的方程为
,点
关于x轴的对称点为
,直线
,
分别与x轴相交于P、Q两点,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a812a9b58ccba331cfd21d244329af01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://img.xkw.com/dksih/QBM/2020/12/24/2621114416979968/2623385264226304/STEM/8dcd37f5f04b48a4af764c5640e9e312.png?resizew=189)
(1)求椭圆Γ的方程;
(2)若直线l经过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/425ff352b0cf9389bbc2fb4538007066.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25dd698d57d1cf239eb8752aecaaa4f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
(3)若直线l的方程为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1110f88d62c2b6415eed3f3f2965269.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b763b6f4f86b652af33e33eeb6d91796.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94e8ac27d63ade4077fdcf7cf136cf71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3668b55ec6c015b1afe1aabb38392a35.png)
您最近一年使用:0次
2020-12-27更新
|
1212次组卷
|
6卷引用:上海市松江区2021届高三上学期期末(一模)数学试题
名校
4 . 已知椭圆
:
(
)过点
,
,且离心率为
.
(1)求椭圆
的方程;
(2)设直线
与椭圆
有且仅有一个公共点
,且与
轴交于点
(
,
不重合),
轴,垂足为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/913f78382630e50543e5f7192cae3ed3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c850811ba59a05e945a665196539a048.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设直线
![](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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.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/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b16c7935a2d04c8d43bde3bba8ed907.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c8d0d72f6792cce3eebfe301ebe180e.png)
您最近一年使用:0次
2021-01-22更新
|
589次组卷
|
6卷引用:北京市东城区2021届高三上学期期末考试数学试题
北京市东城区2021届高三上学期期末考试数学试题(已下线)专题24 椭圆(解答题)-2021年高考数学(文)二轮复习热点题型精选精练(已下线)专题26 椭圆(解答题)-2021年高考数学(理)二轮复习热点题型精选精练(已下线)专题25 椭圆(解答题)-2021年高考数学二轮复习热点题型精选精练(新高考地区专用)河南省洛阳市2021届高三四模数学文科试题河南省新安县第一高级中学2021届高三下学期二练热身练数学(文)试题
名校
解题方法
5 . 已知椭圆
的离心率为
,椭圆
的中心O关于直线
的对称点落在直线
上.
(1)求椭圆
的方程;
(2)设
,M、N是椭圆
上关于x轴对称的任意两点,连接
交椭圆
于另一点E,求直线
的斜率范围并证明直线
与x轴相交定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3427cba868f8176c61c3f58d44f2ab9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b683c0866e725bd30dd41c31149635cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/521e8a2fa5514c407d97b8c292cc406a.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c153027427477bcd0a7228b14ce96cc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c8ffe24cf9f327aeb241225ab15ab1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c8ffe24cf9f327aeb241225ab15ab1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ce6c0e9de83f2e64ae33609fc08459d.png)
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2021-04-01更新
|
1064次组卷
|
5卷引用:海南省海南中学2020届高三数学第九次月考试题
海南省海南中学2020届高三数学第九次月考试题2020届山西省太原市第五中学高三第二次模拟(6月) 数学(理)试题山西省太原五中2020届高三高考数学(理科)二模试题(已下线)专题15 圆锥曲线中的热点问题-备战2021年高考数学二轮复习题型专练(新高考专用)(已下线)专题28 圆锥曲线求范围及最值六种类型大题100题-【千题百练】2022年新高考数学高频考点+题型专项千题百练(新高考适用)
解题方法
6 . 已知椭圆C:
(
)的离心率为
,直线
与椭圆C有且只有一个公共点.
(1)求椭圆C的标准方程
(2)设点
,
,P为椭圆C上一点,且直线
与
的斜率乘积为
,点M,N是椭圆C上不同于A,B的两点,且满足
,
,求证:
的面积为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827ccf0c04aa941ba20d5f4c6068b46b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0d2d0eb98a3265ee04d540f3e59909b.png)
(1)求椭圆C的标准方程
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fca22d434c8671cf39eba5fa03b31ac2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f2d7ff2b15c4e93fe6b92baca3c76d5.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/459c84c9addfbd1cdd0a877ba7c584e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/135642ee219ef29253e7bd35e4f47362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc8c0635e65b4dfedde8b411e5626aae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25dd698d57d1cf239eb8752aecaaa4f4.png)
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7 . 已知中心在直角坐标系的原点,焦点在坐标轴上的椭圆C经过两点
,(0,-3).
(1)求椭圆C的标准方程;
(2)已知点
,过点F(1,0)的直线l交椭圆C于A,B两点,交直线x=10于点P,求证:直线MA,MP,MB的斜率依次构成等差数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1b565f3615ac00bdd2f8ec9c09a7c42.png)
(1)求椭圆C的标准方程;
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bed6e8cafebfb393faed8a4cbded15d.png)
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8 . 椭圆
的离心率为
,上顶点为
,右焦点为
,原点
到直线
的距离为
.
(1)求椭圆
的方程;
(2)直线
为抛物线
的准线,
分别为椭圆的左、右顶点,
为直线
上的任一点(
不在
轴上),
交椭圆
于另一点
交椭圆
于另一点
,求证:
三点共线.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/907d5147cea4c9ce855074864fe54506.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24c14ff9b66f21c05e52dc3c8908c2df.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/562585ef36ef1baa03315e9ec61e8a2b.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a4c25f1295ed707d3723744473eeb39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13ebb1b16a47bcd3d0d847e46126412e.png)
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名校
解题方法
9 . 已知点
为椭圆
上任意一点,直线
与圆
交于
,
两点,点
为椭圆
的左焦点.
(1)求证:直线
与椭圆
相切;
(2)判断
是否为定值,并说明理由.
![](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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0eea02b3e07ba8b9771e9401a81f983.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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36719f1e764ee0e719b65c49fae84677.png)
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2020-04-22更新
|
459次组卷
|
3卷引用:2020届内蒙古呼伦贝尔市海拉尔区高三第一次统考理科数学试题
解题方法
10 . 已知椭圆
的离心率为
,长轴长为
,又已知直线
和点
.
(1)求椭圆
的方程;
(2)若直线
与椭圆
有两个不同的交点,求实数
的取值范围;
(3)若直线
不经过
,且与椭圆
相交于
,
,直线
,
的斜率分别为
,
.求证:
是定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df1dad0690278e2e7c069a27612b7636.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/588c3822b7812e711b4ad86647b15dc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d00a5df9d281dd4e1e45bf6a4d6fb27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5b3a79f33182dc42aee6b04194825af.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若直线
![](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/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5b3a79f33182dc42aee6b04194825af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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