1 . 已知直线
:
.
(1)证明:直线
一定经过第三象限;
(2)设直线
与
轴,
轴分别交于
,
点,当点
离直线
最远时,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b225aabddcbe4f8a5e6fc3ee608ebfa9.png)
(1)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.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/6e9b5e076078240e0c5ad9763a9824d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
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2021-11-05更新
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220次组卷
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2卷引用:河北省高碑店市崇德实验中学2023-2024学年高二上学期9月月考数学试题
2 . 已知λ∈R,求证直线l:(2λ+1)x+(3λ+1)y-7λ-3=0恒过定点,并求出该定点坐标.
您最近一年使用:0次
名校
3 . 已知直线方程为
,其中
.
(1)求证:直线恒过定点;
(2)若直线分别与
轴、
轴的负半轴交于
两点,求
面积的最小值及此时的直线方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/612cdbb392f8bc4bb1c5f40a0f003d29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2725a89d93c791f7a0098f4964587905.png)
(1)求证:直线恒过定点;
(2)若直线分别与
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
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2020-10-15更新
|
638次组卷
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8卷引用:河北省衡水市武强中学2020-2021学年高二上学期第一次月考数学(A)试题
解题方法
4 . 已知椭圆
:
的右焦点为
,离心率为
,过原点的直线
(不与坐标轴重合)与
交于
两点,且
.
(1)求椭圆
的方程;
(2)过
作
轴于点
,连接
,并延长交椭圆
于
,证明以线段
为直径的圆经过点
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/075ba8c6fb5ef7288cd3fed425c8e69e.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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77969a826a095e26d60c13c6d85b369b.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd263fa65347735f95d3364e5b91a58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
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解题方法
5 . 已知双曲线
,
是
上的任意一点.
(1)求证:点
到双曲线
的两条渐近线的距离的乘积是一个常数.
(2)若点
的坐标为
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70886c1a5846ff7a49fd60a507784f6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求证:点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8e32f16d75ccb62a04970f861827fca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ce5dcaffd91bc44cda4a2e44000ae73.png)
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6 . 已知圆
的方程为
,直线
的方程为
,点
在直线
上,过点
作圆
的切线
,
,切点为
,
.
(1)求若
,试求点
的坐标;
(2)求证:直线
过定点;
(3)设线段
的中点为
,求点
的轨迹方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1754846b9b36407340e6e69c381353c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f52cb58b6bc5d71030463ba7e28134.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(1)求若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b15b82151bff7cc0238d2034a6129f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(3)设线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
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名校
7 . 已知
的顶点
,
,
.
(1)求
边上的高
所在直线的方程;
(2)证明:
为等腰直角三角形.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7078a4e8e927c163c7f98e66759c9834.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fcfce809e35760212e25a2acb43e62d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6939f23fec1323cd20c176f835c386a3.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
您最近一年使用:0次
2020-07-23更新
|
210次组卷
|
2卷引用:河北省保定市2019-2020学年高一下学期期末数学试题
8 . 过抛物线
的对称轴上的定点
,作直线
与抛物线相交于
、
两点.
(1)证明:
、
两点的纵坐标之积为定值;
(2)若点
是定直线
上的任一点,设三条直线
,
,
的斜率分别为
,
,
,证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3764ba3aa0a241787f4661026bb14053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf2f0d9868a1a561f6415369cbf5ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02c25e28fd001fbf07c3f3ea2e89a35a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ff131c92aa9e10f696d374216cdcf4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f95cefb160c373407a49e3a8aee1a228.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0721e40e4c6929a24c54d2035c4014a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b1241589f386e0091d54a3c97fd338c.png)
您最近一年使用:0次
2020-07-01更新
|
269次组卷
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2卷引用:2020届河北省新乐市第一中学高三下学期高考冲刺数学试题
9 . 在平面直角坐标系
中,如图所示,已知椭圆
的左、右顶点分别为
,
,右焦点为
.设过点
的直线
,
与此椭圆分别交于点
,
,其中
,
,
.
![](https://img.xkw.com/dksih/QBM/2019/12/28/2365025706655744/2366995827171328/STEM/3e3553f7-3385-41d3-a156-e84cd8e3d90d.png?resizew=242)
(1)设动点
满足:
,求点
的轨迹;
(2)设
,
,求点
的坐标;
(3)设
,求证:直线
必过
轴上的一定点(其坐标与
无关),并求出该定点的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb4717d7fa6d522090c5e949f650bd8.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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/315814ba7b5df22450bbba89c3383cfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e98c4b3f3fe826e124ca7d199d4ca4b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/817a419430d9951cbdb89b657b21bcf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8198c3b302b3820e86763428eb1e91cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3463ced6030af957f13f9ba05b977c1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abcdb7671e6056d842cdc88fb523467f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4399fefbfaa8cf9678cfcc1fe14cf29d.png)
![](https://img.xkw.com/dksih/QBM/2019/12/28/2365025706655744/2366995827171328/STEM/3e3553f7-3385-41d3-a156-e84cd8e3d90d.png?resizew=242)
(1)设动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1638b1aab85dab8ec74648573c7af2b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0736457346c11dd6f458418a4f747ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c723897789dcc3fcbc3ca12a94cee481.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/822921b3e0b6db0ce9c8b4a56043e9e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2019-12-31更新
|
2291次组卷
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4卷引用:河北省廊坊市六校联考2019-2020学年高二上学期期中调研联考数学试题
河北省廊坊市六校联考2019-2020学年高二上学期期中调研联考数学试题2016届四川省双流中学高三12月月考理科数学试卷(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7 圆锥曲线之极点与极线 微点2 极点与极线问题常见模型总结
名校
10 . 已知直线
,
.
(1)证明:直线
过定点;
(2)已知直线
//
,
为坐标原点,
为直线
上的两个动点,
,若
的面积为
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/645df2c7f4860c57ca86acd9defc0945.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a941e4110036577b8e244df3620054df.png)
(1)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
(2)已知直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ff1c07d3ab5f594be5fffe13ebaaccb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b8189f7b0ffe4d20bf0fad43b4ed589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
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2020-02-28更新
|
649次组卷
|
3卷引用:河北省石家庄市第二中学2017-2018学年高一下学期期末数学试题