解题方法
1 . 点在圆
上移动,点
在椭圆
上移动,则线段
的最大值为
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2 . 设双曲线
上两动点
离心角分别为
,若
,试求双曲线在
两点处切线的交点轨迹.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f3fa0b40fb0d9b8c62e37316ab3b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5425108c557f0f21474c045334f97d9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e288596fa3811dd2c17bded60e82e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f60c46676928d20cffd26a8589b5e622.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5425108c557f0f21474c045334f97d9c.png)
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3 . 将平面直角坐标系
中坐标原点O和x轴正半轴保留,y轴去掉,且换x为r便可以得到平面的极坐标系,极坐标为
,其中
为直线
与x轴正向夹角.运用你所学过的数学知识,推测极坐标方程
的图象最可能是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a9e1eb4c3226489d1344321b10b7de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/117854225d787dcd23f2eaf9b36a1a63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c8129e8a922ebdd4baeba38fca270c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f802044475e47cb65d0d1f2d4743826.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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解题方法
4 . 设椭圆
的左、右焦点为
,椭圆上一点
和平面一点
满足
,则
的最大值与最小值之和是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e78f1a9cc4dedc05c175ab99b288b9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9ea91dcba7707db9a70cac100779f43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ef1d66e3bc2f3f0e57af70196ba34b2.png)
A.48 | B.50 | C.52 | D.54 |
您最近一年使用:0次
5 . 如图所示,在平面直角坐标系
中,P是不在x轴上的一个动点,过点P可作抛物线
的两条切线,两切点A、B的连线与
垂直.设直线
与直线
与x轴的交点分别为Q、R.
![](https://img.xkw.com/dksih/QBM/2021/9/24/2815037014687744/2815804218966016/STEM/6577450b-894a-4048-a6d1-ee81f24bcd36.png?resizew=234)
(1)证明:R是一个定点;
(2)求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef49a3ca580a144cc65a609c167facc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef49a3ca580a144cc65a609c167facc1.png)
![](https://img.xkw.com/dksih/QBM/2021/9/24/2815037014687744/2815804218966016/STEM/6577450b-894a-4048-a6d1-ee81f24bcd36.png?resizew=234)
(1)证明:R是一个定点;
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50c707d0350c121c6a611db39a5e85d.png)
您最近一年使用:0次
2021-09-25更新
|
625次组卷
|
3卷引用:2014年全国高中数学联合竞赛试题
6 . 曲线
的极坐标方程是
,点
的极坐标是
,曲线
在平面内绕
旋转一周,则它扫过区域的面积是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a87069ee6af4c4ca77dc4f9787d79bfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fab8a0cc6504aa4c3a38006f5394b4c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
您最近一年使用:0次