Question

已知A,B两点的坐标分别为(0,-5)和(0,5),直线AM与MB的斜率之积为-4/9,则点M的轨迹方程

Answer 1

设点M的坐标为(x,y),

则直线AM的斜率k1 = y /(x +5),

直线BM的斜率k2 = y/(x-5),

k1* k2 =-4/9,

则 y/(x+5) * y/(x-5) =-4/9,

整理得:4x^2+9y^2=100

化为椭圆方程 :x^2/25 + y^2/(100/9)=1.