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解题方法
1 . 已知
的三个顶点分别为
,
,
.求:
(1)
边的中线所在直线
的方程;
(2)
边的中垂线所在的直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40630a669f4eedf626bc24851df10c85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/226fe0c0aadd5d2181ae1796f83b5757.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fa4aeb4b0cdd014a6719ee818d7f521.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
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解题方法
2 . 已知点
,
.
(1)设
,若直线
与直线
垂直,求
的值;
(2)求过点
且与直线
夹角的余弦值为
的直线方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8748dc55e2f45bc37fc4d84d7310f79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7ea6b5f801158380a615c3f99f615e1.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcd9218a657b17654c5d757a6f7dee9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1eea2ca31c4f989e970a18bf8722198.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)求过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04eed461026f69fe9ab2c5dc12af8ac7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9868f77d5ab5073b6145f1c6d272122e.png)
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3 . (1)求过点
且与直线
平行的直线
的方程;
(2)求与直线
垂直,且与两坐标轴围成的
面积为
的直线方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecbe44ef66cee39781307cdee7ef6f1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58742773d6c4c776ce9a233878db15c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e17a2ed1e7f8a43cae08f045dcb9009.png)
(2)求与直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06881a0e74142af188fef42beb4e2c40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
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解题方法
4 . 已知圆C的方程为:
,直线l的方程为:
,
(1)若直线l在两坐标轴上的截距相等,求直线l的方程;
(2)证明:直线l与圆C相交,设直线l与圆C相交于A、B,求弦长
的最小值,及此时直线l的方程;
(3)圆C的圆心C与A、B构成三角形,求三角形ABC面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6149f77c210b79bd8059c7834ed35e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0918b40c288ea327d46f851493be688e.png)
(1)若直线l在两坐标轴上的截距相等,求直线l的方程;
(2)证明:直线l与圆C相交,设直线l与圆C相交于A、B,求弦长
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
(3)圆C的圆心C与A、B构成三角形,求三角形ABC面积的最大值.
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2024-04-07更新
|
305次组卷
|
2卷引用:湖北省宜荆荆随恩2023-2024学年高二下学期3月联考数学试题
名校
解题方法
5 . 已知直线
:
与
垂直,且
经过点
.
(1)求
的一般式方程;
(2)若
与圆
:
相交于
两点,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b3412469e573766c556a98550af8a90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/455ba3d3e46977fcbe5b71f8bb9df4be.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59decaee08ff5ba9047a281d400d2bb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
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2024-03-27更新
|
402次组卷
|
5卷引用:山东省日照市2023-2024学年高二上学期期末校际联合考试数学试题
名校
6 . 已知直线
(1)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)判断直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5582205dd3a4d3cd9b85853fcd60f37b.png)
(3)若直线
![](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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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7 . 设直线l的方程为
.
(1)若直线l在两坐标轴上的截距相等,求直线l的方程;
(2)若
,直线l与x、y轴分别交于M、N两点,求△OMN面积取最值时,直线l的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05c128b62e8817983abad58b0c7e0b5a.png)
(1)若直线l在两坐标轴上的截距相等,求直线l的方程;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df7b5582e1931243dbb90b7591137f23.png)
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解题方法
8 . 求满足下列条件的直线或圆的方程.
(1)求经过点
,且与直线
平行的直线方程;
(2)求经过两条直线
和
的交点,且垂直于
的直线方程;
(3)求半径为
且与直线
相切于点
的圆的方程.
(1)求经过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/643b31966f52a03f001f2e613cd701dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d3ac21cc8b4044ef139c63a0c7e4c9.png)
(2)求经过两条直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c359c48da965e799b9e230578048f975.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9914263ffebdc0aa082603879e8cd847.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/198423f0798da7ce226576b97a1f289e.png)
(3)求半径为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeb73ab4b7d6c79316bc137dd3147c18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cb3e0b614f6571ee55c33ac08c9a4a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad42625f296d2a4b65180e2f7b776beb.png)
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解题方法
9 . 已知
的三个顶点是
,
,
.
(1)求
边上的中线的直线方程;
(2)求
边上的高的直线方程
(3)求AC边的垂直平分线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e95e84f5c91c910aaafc5e74dbfbdf59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29fc95526a39ae87a6e736900fb90e0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dc03fafb03395ed84030f03c5d93aa3.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
(3)求AC边的垂直平分线
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解题方法
10 . 已知直线
:
,
:
,其中
为实数.
(1)当
时,求直线
,
之间的距离;
(2)当
时,求过直线
,
的交点,且垂直于直线
的直线方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c21d0c107654b1241c88267f82225c62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a50d7dca2e767d18989a5094e2ccf1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/027830fc47290062692964077ee481e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.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/091c83390d0755e1b72755cf37490351.png)
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