How do you find the eccentricity of an ellipse given the intersection points with a circle that shares the center with the ellipse?

Question

I was wondering how to find the equation of an ellipse with points that intersect a circle with the same center. I attempted to solve it using these following parameters: (a,b) , (c,d) , (e,f) , (g,h) are the intersection points r is the radius of a circle. Is there any way to solve this?

Answer 1

You can't. In the figure, the two ellipses have the same common points.