Question

(1)抛物线的顶点在原点,焦点是椭圆4x^2+9y^2=36的左焦点,求抛物线方程 (2)抛物线的

Answer 1

椭圆焦点为(√5,0)(-√5,0)

两者同焦点故抛物线方程为y^2=4√5x或y^2=-4√5x

设抛物线为y=kx^2,解得k=-3/4,x^2=-4y/3

设抛物线为x=ky^2,解得k=2/9,y^2=9x/2