名校
1 . 已知椭圆
的短轴长为
,左、右顶点分别为
,过右焦点
的直线
交椭圆
于
两点(不与
重合),直线
与直线
交于点
.
(1)求椭圆
的方程;
(2)求证:点
在定直线上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a200ca2c4af794f4d1c6a5443830b5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092fd1b1d33979818300cd2e3699bff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)求证:点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
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2 . 已知直线
,圆
,下列说法错误 的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17e66d661394a74301296312680c1e62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e01268ac8e838d0f45ccb35bc1d479d0.png)
A.对任意实数![]() ![]() ![]() |
B.当且仅当![]() ![]() ![]() ![]() |
C.对任意实数![]() ![]() ![]() |
D.存在实数![]() ![]() ![]() |
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3 . 已知抛物线
的焦点为F,准线与x轴的交点为A,点B在C上.若
,则直线AB的方程为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dc35b7e6cdf04d4fa832ddef4ffef07.png)
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2024-06-10更新
|
388次组卷
|
2卷引用:北京市中国人民大学附属中学2024届高三下学期5月热身练习数学试题(三模)
名校
解题方法
4 . 已知
,若点P满足
,则点P到直线
的距离的最大值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f01b186ac8aa73e1a3609b40b6c3ee6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83640592853a53872d7af69c0cffc1bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff5be0fcefb76a1958f482205475b351.png)
A.1 | B.2 | C.3 | D.4 |
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2024-06-10更新
|
545次组卷
|
2卷引用:北京市中国人民大学附属中学2024届高三下学期5月热身练习数学试题(三模)
名校
解题方法
5 . 已知O为坐标原点,椭圆
上一点D的横坐标为1,斜率存在的直线l交椭圆C于A,B两点,且直线DA,DB的斜率之和等于1.
(1)求
;
(2)若点D在第一象限,探究
的面积是否有最大值?若有,求出最大值;若没有,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85d84072e42ab4af37340ee0906535ef.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e2288109e13b7dd099f8dba9bd4997c.png)
(2)若点D在第一象限,探究
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2b83beedb3438153e6f728545fe3e03.png)
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解题方法
6 . 已知曲线
为坐标原点.给出下列四个结论:
①曲线
关于直线
成轴对称图形;
②经过坐标原点
的直线
与曲线
有且仅有一个公共点;
③直线
与曲线
所围成的图形的面积为
;
④设直线
,当
时,直线
与曲线
恰有三个公共点.其中所有正确结论的序号是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad59807e7700def79ad947b88d8c4dcd.png)
①曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
②经过坐标原点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
③直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3070c679fb57d37e2224c5205fd3812.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/015c9ed38ba5b709c5d51102857cd905.png)
④设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94a8d6991873e79b298984a95b8954b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d69fa853794ba03bf379140ecccf59c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
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2024-05-07更新
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462次组卷
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3卷引用:北京市昌平区2024届高三第二次统一练习数学试题
7 . 直线
截圆
所得劣弧所对的圆心角为
,则r的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4958a3ab5b7a862f715b14822710b6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b1eeecbc0147648a0d48808eebda305.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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8 . 在平面直角坐标系
中,已知
为圆
上动点,则
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d45ffc2aab28c1a42e70ee3d0a5ca5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a7e74305038711eb557a91bcf955c54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a430c41f782c5c12f68a49c5d0cb1ee2.png)
A.34 | B.40 | C.44 | D.48 |
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2024-04-08更新
|
631次组卷
|
2卷引用:北京市通州区潞河中学2023-2024学年高三下学期第三次模拟数学试卷
名校
9 . 设点
在抛物线
上,已知
.若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14bd426e7e1e65d91394da0b28d49f65.png)
__________ ;若
,则直线
斜率的最小值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7775aa57ca0e62216f3039ed88dceed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22ac6188f40414f76bc754dee4a75809.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e48b0ba6fbb831b99e0868a3c91cafa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a79a4c82b46d2032adfb0659c7434cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14bd426e7e1e65d91394da0b28d49f65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee21db6628e4db3f5831370549fa96b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
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2024-04-03更新
|
576次组卷
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2卷引用:北京市北师大附属实验中学2024届高三下学期3月零模数学试题
10 . 在平面直角坐标系中, 记
为点
到直线
的距离, 则当
变化时,
的最大值与最小值之差为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a39eb343f10b190dcba68fd1e8bb37f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdee4045d21a57f58bdbc7a3183d5f5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85952754cbc607e5a0d01332cd26be83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
A.2 | B.3 | C.4 | D.6 |
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