1 . 参数方程是以参变量为中介来表示直线或曲线上点的坐标的方程,是直线或曲线在同一坐标系下的另一种表现形式.很多曲线(如心脏线、螺线、玫瑰线)都可以用参数方程呈现.在平面直角坐标系
中,直线
的参数方程式
(
为参数),其中
,角
为直线
的倾斜角.曲线
的参数方程是
(
为参数).其中
,直线
与曲线
相交于
、
点.
(1)根据以上的参数方程求出直线
的一般式方程和曲线
的标准方程;
(2)设点
,设点
对应的参数为
,试证明:
;
(3)试问是否存在角
,使得对于任意的点
,表达式
均为定值
,若存在,请求出
及值
(结果用
,
表示);若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9b1cf149172b6c4a6526b25aba683be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1d5e2dfa2d5b134c85995877eff156b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73dd51ce19cf9b0ebfa8e42190c72bbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.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/e77eee60e92c3e08a5877062cd1e925f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a990942b9fa26d28cee8579325da3675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(1)根据以上的参数方程求出直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93bb2baf350ed7e3490fd9e7399ce5c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d9fd58e71dcae6cafaf9037d20ebd76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39b1c2f6f5103b4a981e417b620dd239.png)
(3)试问是否存在角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93bb2baf350ed7e3490fd9e7399ce5c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6df16c0ff148acd2c4eac082120e43be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291f17141e5dfbb8e129a9e59d23c120.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
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解题方法
2 . 已知F为抛物线
(t为参数)的焦点,过F作两条互相垂直的直线
,直线
与C交于A,B两点,直线
与C交于D,E两点,则
的最小值为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/512d63e6d79877f4407a6a8f68dce3e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.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/192aeb9fe486f44a27d837274daf8657.png)
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陕西省2024届高三教学质量检测(一)文科数学试题陕西省2024届高三教学质量检测(一)理科数学试题(已下线)第2章 圆锥曲线 单元综合检测(难点)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)
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3 . 已知曲线
的参数方程为
(
为参数),直线
过点
.
(1)求曲线
的普通方程;
(2)若直线
与曲线
交于
,
两点,且
,求直线
的倾斜角.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a4c4c9cf8f0bd3f84fdc5bae0aa65b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1b6f209d1a805437046ca6ef79dd.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若直线
![](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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffea71f4a401758f650444e16c10d017.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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解题方法
4 . 实数
满足
,则
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d10449bc77d692a7270e0f20a68cdf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d63471465a852901b6aaf6b7fc4d042.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e159c8203722a3c50784f7f6e65911e2.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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解题方法
5 . 在直角坐标系
中,直线
的参数方程为
(
为参数
).以坐标原点
为极点,
轴的正半轴为极轴建立极坐标系,半圆
的极坐标方程为
.
(1)求半圆
的参数方程和直线
的直角坐标方程;
(2)直线
与
轴交于点
,与
轴交于点
,点
在半圆
上,且直线
的倾斜角是直线
的倾斜角的
倍,
的面积为
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ed96b80b51308e0df26ec8d5be3bcad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11186de3f6a870c3702f5ac18513b9ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12f102439ebd1efd422f04209ecec2bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.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/d91659906d952d03eac315b6f062548a.png)
(1)求半圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0fe1e989d7fe8a9eb35cb5cf0f9cdaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
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