设点M的坐标为(x,y)
|sqrt[(x-c)^2+y^2]|/|x-a^2/c|=c/a c>0,c/a>1
两边平方得
a^2[(x-c)^2+y^2]=c^2(x-a^2/c)^2
a^2x^2-2a^2cx+a^2c^2+a^2y^2=c^2x^2-2a^2cx+a^4
(c^2-a^2)x^2-a^2y^2=a^2(c^2-a^2)
x^2/a^2-y^2/(c^2-a^2)=1
为双曲线.