已知椭圆(x^2)/2+y^2=1,过点A(2,1)的直线l与椭圆相交,求l被截得的弦的中点轨迹方程.
人气:130 ℃ 时间:2019-09-09 17:21:59
解答
可设直线方程为y-1=k(x-2) (k≠0,否则与椭圆相切),设两交点分别为(x1,y1),(x2,y2),则x1^2/2+y1^2=1,x2^2/2+y2^2=1,两式相减得(x1+x2)(x1-x2)/2+(y1+y2)(y1-y2)=0,显然x1≠x2(两点不重合),故(x1+x2)/2+(y1+y2)(y1...
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