1 . 设椭圆C:
的左、右顶点和椭圆
的左、右焦点均为E,F.P是C上的一个动点(异于E,F),已知直线EP交直线
于点A,直线FP交直线
于点B.直线AB与椭圆
交于点M,N,O为坐标原点.
(1)若b为定值,证明:
为定值;
(2)若直线OM,ON的斜率之积恒为
,求b.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd8c4b0e11e5894346b27e4656336c67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9e7a9b887d3dca1953a4f271d7b60a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f09e84f509537abd3dfaa20d7915675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee023dde0cd66b17a3ec5775d4b7d714.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(1)若b为定值,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2b0ba14e41e306e5633ad4bf1cdedd8.png)
(2)若直线OM,ON的斜率之积恒为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3389f53711264b0acba3ba6019f8b908.png)
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解题方法
2 . 已知椭圆的焦点是椭圆
的顶点,椭圆
的焦点也是
的顶点.
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/654317ca05d25fee978869723ba8d0c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/937c5db73d81da5525d4d35885dac04f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8112f9185c7d48b015d9cd0525616b31.png)
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3 . 已知抛物线
:
和椭圆
:
有共同的焦点F
(1)求抛物线C的方程,并写出它的准线方程
(2)过F作直线
交抛物线C于P, Q两点,交椭圆E于M, N两点,证明:当且仅当
轴时,
取得最小值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089148c36cb3c39af71de653756396a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c117fd51ea6f0a5a0c45077a137ef777.png)
(1)求抛物线C的方程,并写出它的准线方程
(2)过F作直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/165a501b2e6a3acc46212e59a166c053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cff8d039dd1991c12d2de58d1dc2937a.png)
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4 . 已知双曲线
的左、右焦点分别为
,
,且与椭圆
有相同的焦点,点
到直线
的距离为
.
(1)求
的标准方程;
(2)直线
与
交于
两点,点
是
的平分线上一动点,且
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a2cfa22139b3e9c9a73500e1ba19f52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5076829e649b3f3866d4a7e07a5713e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/697c20fca284394bf5d5b9e5f6d952e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e78f1a9cc4dedc05c175ab99b288b9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4769228ab5c2538da39d7490e11070c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65433a90ddb846316dd8094d3ef38cbd.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3f1b91f32240e9c01de1ea042422cac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66abb7d52b61f0f325af76e425bbb5eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69a564e580b866c00d279a59ec49cb06.png)
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2022-11-10更新
|
414次组卷
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4卷引用:河北省部分学校2022-2023学年高二上学期期中数学试题
名校
解题方法
5 . 在平面直角坐标系
中,已知椭圆
:
的离心率为
,椭圆的右焦点与抛物线
的焦点重合,过点
(
,
)且不垂直于x轴y轴的直线与椭圆C交于A,B两点,点
为椭圆C外一点,且
.
(1)求椭圆C的方程;
(2)
是否为定值?若是定值,求出该定值,并给出证明;若不是定值,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84bfec4efcc9f0e656d6864daaaef55d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b26e6e910d5fdd1e28a8ca357ae4c732.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0baedc4d7e690ab3f7d80d30ba0a9efe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be20a7210b16723d7d9a943ecca4c3de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba069fd3d0a8244e67f42c73e255d52f.png)
(1)求椭圆C的方程;
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1019d4ad2e3fb4a7abb66e0e9e55b556.png)
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2021-09-18更新
|
372次组卷
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2卷引用:河北省沧州市第一中学等十五校2022届高三上学期摸底考试数学试题