解题方法
1 . 已知椭圆
的离心率为
,两焦点
,
与椭圆上的顶点
构成边长为2的等边
.
(1)求椭圆
的方程;
(2)过点
的直线
与
相交于
,
两点,在
轴上是否存在点
,使得
为定值?如果有,求出点
的坐标及定值;如果没有,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.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/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91fbc9b62f2e82af009bd2f4587969fb.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7a999c36de5c9a9ce876a4a56fa34c.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4272df1f9ea5ee9b2843d1886477a42a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
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2021-09-10更新
|
1852次组卷
|
4卷引用:云南省富宁县第一中学2020-2021学年高二下学期第三次月考数学(理)试题
云南省富宁县第一中学2020-2021学年高二下学期第三次月考数学(理)试题云南省富宁县第一中学2020-2021学年高二下学期第三次月考数学(文)试题(已下线)第11讲 椭圆(6大考点)-2022-2023学年高二数学考试满分全攻略(人教A版2019选修第一册)(已下线)专题31 圆锥曲线存在性问题的五种类型大题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
2 . 已知直线
与抛物线
相交于
、
两点,则
的长为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33400b08941f4f9c0ed12b0e0cdff822.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c1ba86ffc6e5542b62319848c14acaa.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/aaff41080fdea43eea7efedf9ebc1498.png)
A.12 | B.16 | C.7 | D.8 |
您最近一年使用:0次
解题方法
3 . 已知椭圆的中点在原点,焦点在x轴上,长轴长为12,离心率为
,则椭圆的方程为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
解题方法
4 . 已知曲线
:
,焦点是
,
是抛物线上任意一点,则点
到焦点
和到点
的距离之和的最小值是_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39ea1f5bdd213c7c3a571b4c38850bf1.png)
您最近一年使用:0次
解题方法
5 . 已知过点
的曲线
的方程为
.
(1)求曲线
的标准方程:
(2)已知点
,
为直线
上任意一点,过
作
的垂线交曲线
于点
,
.证明:
平分线段
(其中
为坐标原点).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/711ca77eefc53ea6784a4fdfdcf4827c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/013f7960dd5c782520835afa52465ae6.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/055a2ef09e2ee0948cf67c58de58732d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
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解题方法
6 . 双曲线
的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7761143e895d70faee67e3185a6098cb.png)
A.![]() | B.3 | C.![]() | D.![]() |
您最近一年使用:0次
2021-09-02更新
|
174次组卷
|
2卷引用:云南省南涧县第一中学2020-2021学年高二下学期数学(理)期中考试题
解题方法
7 . 如图,点
为抛物线
的焦点,直线l过点F且与抛物线交于A,B两点(A在B的上方),与抛物线的准线交于点C,若
,则l的斜率为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089148c36cb3c39af71de653756396a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93db7a67168363e3b35751550f68ab26.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/8/abc3f70e-8f35-4443-914b-58312767d962.png?resizew=198)
您最近一年使用:0次
解题方法
8 . 已知椭圆
过点
,且焦距为
.
(1)求椭圆C的方程;
(2)不经过点P的直线l与椭圆C交于A,B两点,直线PA,PB的斜率之积为6.若l的斜率为
,求直线PA的斜率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef404abca1f78da130a38849f58559.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e9b5e076078240e0c5ad9763a9824d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
(1)求椭圆C的方程;
(2)不经过点P的直线l与椭圆C交于A,B两点,直线PA,PB的斜率之积为6.若l的斜率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a2008b78a906cf5ecdfd68432fa9ad1.png)
您最近一年使用:0次
2021-09-02更新
|
162次组卷
|
2卷引用:云南省南涧县第一中学2020-2021学年高二下学期数学(理)期中考试题
9 . 已知命题
抛物线
的焦点为
;命题
平面内两条不同直线的斜率相等是两条直线平行的充分不必要条件.则下列命题是真命题的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51441c8788ff11be766766227793246d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/108c18cb76d7d34b05c991a644c8b136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34441124c1aae3bf35f76ae1b31451fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce20ef9c08e82df8c7f45bac6dd31d36.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
解题方法
10 . 如图,已知直线
与抛物线
相切于点
,且与
轴交于点
,定点
的坐标为
.
![](https://img.xkw.com/dksih/QBM/2021/4/28/2709693311049728/2798224034119680/STEM/bfd7bd2d-b053-47c6-8ff1-25abc8baa85b.png?resizew=195)
(1)求以
为左焦点且过点
的椭圆
的标准方程;
(2)若过点
的直线
(斜率不等于零)与(1)中的椭圆
交于不同的两点
,
(
在
,
之间),试求
与
面积之比的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42102c1c07562853219ca5918803a27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f40d5459e1385ab7d829ea96ca0b946.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fab8a0cc6504aa4c3a38006f5394b4c2.png)
![](https://img.xkw.com/dksih/QBM/2021/4/28/2709693311049728/2798224034119680/STEM/bfd7bd2d-b053-47c6-8ff1-25abc8baa85b.png?resizew=195)
(1)求以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7b3560b239bca664c50848502cc878b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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/1bf7264407abc7b2e3b2ef4baa13da06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3954beda5772eb8d5de1002ddeb81524.png)
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