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解题方法
1 . 如图,在平面直角坐标系中,
分别为双曲线Г:
的左、右焦点,点D为线段
的中点,直线MN过点
且与双曲线右支交于
两点,延长MD、ND,分别与双曲线Г交于P、Q两点.
![](https://img.xkw.com/dksih/QBM/2021/12/16/2873675367243776/2876742357467136/STEM/358abcbb-a95a-4f0c-b8e8-023529854af5.png?resizew=211)
(1)已知点
,求点D到直线MN的距离;
(2)求证:
;
(3)若直线MN、PQ的斜率都存在,且依次设为k1、k2.试判断
是否为定值,如果是,请求出
的值;如果不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5848e50805496263d52dcbde9671a89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/438b087a3b66f48298b5a944629adb44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d7d5b7a335fb30a034976287aee9e05.png)
![](https://img.xkw.com/dksih/QBM/2021/12/16/2873675367243776/2876742357467136/STEM/358abcbb-a95a-4f0c-b8e8-023529854af5.png?resizew=211)
(1)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a5261c3908257dfc70e84ae8126163e.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eab0357b5e80a6fa5b1c51a2f01be14.png)
(3)若直线MN、PQ的斜率都存在,且依次设为k1、k2.试判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2a3f348a942d468f0d77c0dfbb41d87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2a3f348a942d468f0d77c0dfbb41d87.png)
您最近一年使用:0次
2021-12-20更新
|
1280次组卷
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5卷引用:上海市闵行区2022届高三上学期一模数学试题
上海市闵行区2022届高三上学期一模数学试题上海市向明中学2022-2023学年高二下学期期中数学试题(已下线)重难点05 解析几何-2022年高考数学【热点·重点·难点】专练(新高考专用)(已下线)押全国卷(理科)第20题 圆锥曲线-备战2022年高考数学(理)临考题号押题(全国卷)(已下线)专题19 圆锥曲线 (模拟练)-2
20-21高三·上海浦东新·阶段练习
2 . 已知
,如图,曲线
由曲线
和曲线
组成,其中点
,
为曲线
所在圆锥曲线的焦点,点
,
为曲线
所在圆锥曲线的焦点.
![](https://img.xkw.com/dksih/QBM/2021/1/16/2637229551067136/2639495255392256/STEM/f414e3ca-8fb7-494b-b1a0-500e2d6e6c5f.png?resizew=332)
(1)若
,
,求曲线
的方程;
(2)如图,作直线
平行于曲线
的渐近线,交曲线
于点
,
,求弦
的中点
的轨迹方程;
(3)对于(1)中的曲线
,若直线
过点
交曲线
于点
,
,求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9398fbc4f06358c41cdd7e93b1407577.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9f05b99371106ae288f01405213be3b.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/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1282962a17a48a18edf733204054d67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/287adcb739a4890d108dd974358345fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://img.xkw.com/dksih/QBM/2021/1/16/2637229551067136/2639495255392256/STEM/f414e3ca-8fb7-494b-b1a0-500e2d6e6c5f.png?resizew=332)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16fd15503ee692f8286b0312f7c6f0cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/804b93b0751acdaec26c8ff4fe9d4148.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
(2)如图,作直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(3)对于(1)中的曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/287adcb739a4890d108dd974358345fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.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/dbdbb45d7359537458736c9ea5bf9e1d.png)
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3卷引用:上海市浦东新区华东师范大学第二附属中学2021届高三4月高考数学模拟试题
3 . 连结双曲线
与
的四个顶点的四边形面积为
,连结四个焦点的四边形面积为
,则
的最大值是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f3fa0b40fb0d9b8c62e37316ab3b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d960ceb806d32113df2bc1b104d2660.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/235f0a6fb218d28383e6f27f2df1f50f.png)
A.2 | B.4 | C.![]() | D.![]() |
您最近一年使用:0次
2017-11-30更新
|
1155次组卷
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3卷引用:沪教版(上海) 高二第二学期 新高考辅导与训练 第12章 圆锥曲线 12.6(2) 直线与双曲线的位置关系
4 . 双曲线
的左右两焦点分别是
,若点
在双曲线上,且
为锐角,则点
的横坐标的取值范围是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb7ccc0565e3cb6cf4aaded0ed10da0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/882651b776851f3f0665de12da6ed47d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40a7c9c4ed8193d12fb425019e0a3466.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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5 . 如图,已知双曲线
的右焦点为
,点
分别在
的两条渐近线上,
轴,
,
(
为坐标原点).
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/10/2084410a-ff89-4705-8aae-fb9c2f500c63.png?resizew=168)
(1)求双曲线
的方程;
(2)过
上一点
的直线
与直线
相交于点
,与直线
相交于点
,证明:点
在
上移动时,
恒为定值,并求此定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d425a7131017df2ef6eb55cc7070caf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/323232ab36943d1d5d2831d70ffcff87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ed285b1d0a7c3e8acf6e5af53265121.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d824d42dc91f81abde6d1c0a72273c1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/10/2084410a-ff89-4705-8aae-fb9c2f500c63.png?resizew=168)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/021bcc5ea186cd32c39b3d333b0f448c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9033efb0903cd79ebd4edf43e42249e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d599059e6b2c918ab15ee22611b6962.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35dc962d118cd70c761f7870b3e59c2d.png)
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7卷引用:沪教版(上海) 高三年级 新高考辅导与训练 第二部分 走近高考 第十章 坐标平面上的直线与线性规划高考题选
沪教版(上海) 高三年级 新高考辅导与训练 第二部分 走近高考 第十章 坐标平面上的直线与线性规划高考题选上海市大同中学2020-2021学年高二下学期开学考试数学试题2014年全国普通高等学校招生统一考试理科数学(江西卷)(已下线)第44讲 解析几何中的极点极线问题-2022年新高考数学二轮专题突破精练(已下线)专题44 盘点圆锥曲线中的定值问题——备战2022年高考数学二轮复习常考点专题突破(已下线)重难点13六种双曲线解题方法-1(已下线)考向36 直线与圆锥曲线最全归纳(十六大经典题型)-3