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解题方法
1 . 已知椭圆
,其上顶点为
;
(1)若直线
与椭圆
交于
、
两点,求证:
为定值;
(2)由椭圆
上不同三点构成的三角形称为椭圆的内接三角形,现以
为直角顶点作椭圆
的内接等腰直角三角形,求内接等腰直角三角形的个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb4402aeb853b22f20992156957ef0fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(1)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/667ac0afa44e3cbba0b90ce891c6a9be.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/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5f6c5fd93aed88bec58002a20ea2e90.png)
(2)由椭圆
![](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)
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2 . 如图,圆
与
轴切于点
,与
轴正半轴交于
两点.点
在点
的下方,且
.
![](https://img.xkw.com/dksih/QBM/2020/5/2/2453956687749120/2454864123715584/STEM/bed54e9d2ce04d7eb21e1f61b3116f08.png?resizew=218)
(1)求圆
的方程;
(2)过点
作一条直线与椭圆
相交于
两点,连接
,求证:
.
![](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/3b45d68e7ef26c34a15988283610c95c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7490886e2807c7b8a4fa57d99c4dc3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03f4840c22eb33c7e7115ff911a96be6.png)
![](https://img.xkw.com/dksih/QBM/2020/5/2/2453956687749120/2454864123715584/STEM/bed54e9d2ce04d7eb21e1f61b3116f08.png?resizew=218)
(1)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cae00bdc6f8b564b6b15b32572c848b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fb398137779190b35492d9f06d5fbc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35acbc816706f5349e123e12eb25ea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d5ce23462dfd28929430b74b9590940.png)
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名校
3 . 已知椭圆G:
的右焦点为F,过F的直线l交椭圆于A、B两点,直线与l不与坐标轴平行,若AB的中点为N,O为坐标原点,直线ON交直线x=3于点M.
(1)求证:MF⊥l;
(2)求
的最大值,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e36bfcf494549dc07de73b3978b8cb42.png)
(1)求证:MF⊥l;
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e368cae5a81dd423b260900fec41071.png)
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名校
4 . 已知直线l与抛物线
交于点A,B两点,与x轴交于点M,直线OA,OB的斜率之积为
.
(1)证明:直线AB过定点;
(2)以AB为直径的圆P交x轴于E,F两点,O为坐标原点,求|OE|
|OF|的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fa2c731aaa4005382d5b4324e29fbb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3389f53711264b0acba3ba6019f8b908.png)
(1)证明:直线AB过定点;
(2)以AB为直径的圆P交x轴于E,F两点,O为坐标原点,求|OE|
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c97ec04a1aa7ac6fce72d589864940a2.png)
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2018-11-25更新
|
585次组卷
|
3卷引用:华中师范大学第一附属中学2018-2019学年高二上学期期中检测理科数学试题
解题方法
5 . 已知椭圆的中心为原点,焦点在
轴上,离心率为
,且经过点
,直线
交椭圆于异于M的不同两点
.直线
轴分别交于点
.
(1)求椭圆标准方程;
(2)求
的取值范围;
(3)证明
是等腰三角形.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3ba9d9535a1d7e34f66db9da0861394.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d00a5df9d281dd4e1e45bf6a4d6fb27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/677a5973ae6d126f3660b776a007a1a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cf9b288c48c73463a2f214f02b6952a.png)
(1)求椭圆标准方程;
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eadb6f330e2d5325adb08c2b1d80b1ae.png)
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