名校
解题方法
1 . 已知点
是抛物线
的焦点,
的两条切线交于点
是切点.
(1)若
,求直线
的方程;
(2)若点
在直线
上,记
的面积为
的面积为
,求
的最小值;
(3)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a51cfe6b1f93e8beab2a1391fa5b8a.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33c767183fcb90fd994f705fa0bebd33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c608def11fa0e2b34f05592ef1d11fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bfbf105868ad7dca03b9663a01c3422.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c74b2b7a4048782fecb0126119bb5dd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/884d40a97fd767e95f34f3b91ab8d84c.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df1e767d0df819ecd47359fee289efc3.png)
您最近一年使用:0次
2024-05-28更新
|
738次组卷
|
2卷引用:广东省广州市2024届普通高中毕业班综合测试(二)广州二模数学试卷
名校
解题方法
2 . 根据下列条件,分别求直线
的方程
(1)直线
经过点
,且与直线
的夹角等于![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e5fa72f2878b476bc57f0df12d6555.png)
(2)经过
与
的交点,且点
到直线
的距离为3
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(1)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b02af485e17e7628fd5a3ace6e0a32ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1927282fd2b7c51533f9a0d0cce7b05c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e5fa72f2878b476bc57f0df12d6555.png)
(2)经过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bc9e7368e59d91d6017e5d4ddbd01fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c5cfc6bd7ba9e8f70ac5135dd8d06ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e358239cdfa5078bcecf62bb1739577.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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名校
3 . 已知拋物线
和
,其中
.
与
在第一象限内的交点为
.
与
在点
处的切线分别为
和
,定义
和
的夹角为曲线
的夹角.
(1)若
的夹角为
,
,求
的值;
(2)若直线
既是
也是
的切线,切点分别为
,当
为直角三角形时,求出相应
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39eebc6a2c5bab554e6fa43c15d60728.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d1138c04fc3a0e1c217db0d432e4aff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](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/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e9feabc99f62ee569b460e61526e2e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e9feabc99f62ee569b460e61526e2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/950ebd2fdaf9e6f461c3ac713f3fea52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9fce9427c9b17e4d3cda0c3ff3e2e14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8ca00309261a540934d9b3ed9ba05b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c28abb154f41e1ca9816c9c9c2433ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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4 . 如果直线与椭圆只有一个交点,称该直线为椭圆的“切线”.已知椭圆
,点
是椭圆
上的任意一点,直线
过点
且是椭圆
的“切线”.
![](https://img.xkw.com/dksih/QBM/2018/4/21/1928762712571904/1933011921952768/STEM/6be1dbf731df4f728a3257ae648f5db8.png?resizew=242)
(1)证明:过椭圆
上的点
的“切线”方程是
;
(2)设
,
是椭圆
长轴上的两个端点,点
不在坐标轴上,直线
,
分别交
轴于点
,
,过
的椭圆
的“切线”
交
轴于点
,证明:点
是线段
的中点;
(3)点
不在
轴上,记椭圆
的两个焦点分别为
和
,判断过
的椭圆
的“切线”
与直线
,
所成夹角是否相等?并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/533b93dd6eb6b474481247736699c76c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc5dd4d07e2098d8d1b731f2622867f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://img.xkw.com/dksih/QBM/2018/4/21/1928762712571904/1933011921952768/STEM/6be1dbf731df4f728a3257ae648f5db8.png?resizew=242)
(1)证明:过椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc5dd4d07e2098d8d1b731f2622867f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6900a40dabd963c43735c21e16cc8ef8.png)
(2)设
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc5dd4d07e2098d8d1b731f2622867f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b66a5b7813e902306477f91f9f4084cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5c62f22d7afc5627fcb86599faa8e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
(3)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc5dd4d07e2098d8d1b731f2622867f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a61d572ecf27dc02fcbd588f24647b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b67528f875a6d4bac8bbf784f7b66a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e1c16e3b7946038eae6be99b0981918.png)
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