题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022232139-31823.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022232140-48256.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022232140-61694.png)
解析
研究直线与圆的相交弦问题,那么联立方程组可知
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022232139-31823.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022232140-48256.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022232140-14179.png)
那么结合韦达定理得到A(-1,0),B(
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022232140-38814.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022232140-70179.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022232141-13027.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022232141-27520.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022232140-61694.png)
解决该试题的关键是利用直线与圆的方程联立方程组,结合韦达定理得到AB的中点坐标,利用直线的垂直关系得到AB的垂直平分线的斜率,得到方程。
核心考点
举一反三
设有半径为3
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022232134-55926.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022232134-20214.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022232134-84065.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022232134-84065.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022232134-20214.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022232134-84065.png)
(1)若
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022232134-20214.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022232134-55926.png)
求:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022232134-20214.png)
(2)设
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022232134-20214.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022232134-84065.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022232135-77060.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022232134-20214.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022232134-84065.png)
(以村落中心为参照,说明方位和距离)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022232135-28533.png)
已知圆
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022232120-35552.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022232120-13869.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022232121-70936.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022232121-61437.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022232121-22759.png)
是
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022232121-74703.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022232121-93341.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022232121-69213.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022232122-37627.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022232122-57613.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022232121-93341.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022232120-35552.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022232122-39479.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022232122-94934.png)
(1)若
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022232122-83646.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022232122-94907.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022232122-39479.png)
(2)经过
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022232122-81972.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022232123-26514.png)
①将
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022232123-67756.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022232121-69213.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022232123-24307.png)
②求线段
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022232123-13823.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022232123-79333.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022232112-33908.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022232112-84272.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022232112-50409.png)
A.(![]() | B.(![]() ![]() | C.(0,![]() | D.(![]() ![]() |
(1)过C1的左顶点引C1的一条渐近线的平行线,求该直线与另一条渐近线及x轴围成的三角形的面积;
(2)设斜率为1的直线l交C1于P、Q两点.若l与圆x2+y2=1相切,求证:OP⊥OQ;
(1)求曲线C1的方程;
(2)设P(x0,y0)(y0≠±3)为圆C2外一点,过P作圆C2的两条切线,分别与曲线C1相交于
点A,B和C,D.证明:当P在直线x=﹣4上运动时,四点A,B,C,D的纵坐标之积为定值.
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