已知椭圆:
,过椭圆左顶点
的直线
交抛物线
于
两点,且
,经过点
的直线
与椭圆交于
两点,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/00fb9428-3831-41ef-9191-da7f5daccf02.png?resizew=176)
(1)求点
的横坐标;
(2)求四边形
的面积最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba375d9ec72546383628b958cb80d4fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089148c36cb3c39af71de653756396a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab609a6574633ebabcff3e73fa862081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfe1e653e100507e6a48ee57875e1701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e1e4115d78e625e9e0f47cdade3286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3a2efbce946ae0e129194b83cdda8d8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/00fb9428-3831-41ef-9191-da7f5daccf02.png?resizew=176)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)求四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/945e93c9f3515ded840de09a9ba81ce8.png)
更新时间:2022-03-23 07:26:12
|
相似题推荐
【推荐1】已知椭圆
的左、右焦点分别为
是
上一动点,
的最大面积为
.
(1)求
的方程;
(2)若直线
与
交于
两点,
为
上两点,且
,求四边形
面积的最大值.
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(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baabfd32465e9e50409413d9c1358279.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
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【推荐2】已知椭圆C:
短轴长为2,左、右焦点分别为
,
,过点
的直线l与椭圆C交于M,N两点,其中M,N分别在x轴上方和下方,
,
,直线
与直线MO交于点
,直线
与直线NO交于点
.
的坐标为
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(2)在(1)的条件下,过点
并垂直于x轴的直线交C于点B,椭圆上不同的两点A,D满足
,
,
成等差数列.求弦AD的中垂线的纵截距的取值范围;
(3)若
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/347b68f42934c74e0d759a67613a1da9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
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(2)在(1)的条件下,过点
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/290b64ccb8a211698c1f03997f0b3b2e.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b04a1eec4fa5ce0544e4e22693b2d3f0.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78bdcd65ef5bffda1f1e993176e43bef.png)
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解答题-问答题
|
困难
(0.15)
【推荐1】已知抛物线
过点
,直线
过抛物线
的焦点
且与抛物线
相交于
、
两点.
![](https://img.xkw.com/dksih/QBM/2020/8/26/2536413920223232/2542583666483200/STEM/1485abc999c04b38a479e3e611cb5f86.png?resizew=160)
(1)若
与
的面积之比为
,求此时直线
的方程;
(2)若与直线
垂直的直线
过点
,且与抛物线
相交于点
、
,设线段
、
的中点分别为
、
,如图,求点
到直线
距离的最大值及此时直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7df40ba57bb5819b4aaa38d514500052.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d70d03665d0f7c841d167788d8eb50d2.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/a0ed1ec316bc54c37c4286c208f55667.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://img.xkw.com/dksih/QBM/2020/8/26/2536413920223232/2542583666483200/STEM/1485abc999c04b38a479e3e611cb5f86.png?resizew=160)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/667724ae7306b56b60defdabf019fe90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29ac8c0f7b41c5f74206e0524a23c31a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbe103f073845122c66f22dcb14b711f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)若与直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
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解答题-问答题
|
困难
(0.15)
名校
解题方法
【推荐2】已知抛物线
,直线
与抛物线
交于
为抛物线
上一点.
(1)若
,求![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
(2)已知点
,过点
作直线
分别交曲线
于
,证明:在点
运动过程中,直线
始终过定点,并求出该定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fa2c731aaa4005382d5b4324e29fbb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33400b08941f4f9c0ed12b0e0cdff822.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23a234cf1ad4edfd5553004d5167fff2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d3835e6398d18d162afebc92cd2ae9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/499a1cdf00140d4d3a085502601cce3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dedd84baa5219a2af415be51947c301.png)
您最近一年使用:0次