Question

椭圆方程!已知椭圆C1:x^2/a^2+y^/b^2=1(a>b>0)的右焦点F与抛物线C2:y^2=4x的焦点重合,椭

Answer 1

抛物线C2:y^2=4x的焦点F的坐标为(1,0),

=>a^2-b^2=1……(1)

|PF|与P到抛物线准线x=-1的距离相等,

故P的横坐标为2/3,=>P纵坐标为根号下8/3

P点坐标代入椭圆方程得

4/(9a^2)+8/(3b^2)=1……(2)

联立(1),(2)解方程组得a^2=4,b^2=3

椭圆C1的方程为:x^2/4+y^/3=1