Problem #64

A ray of light starting at the center of the ellipse
whose equation is
x^{2}/4 +
y^{2} = 1
reflects off the ellipse, moves vertically, reflects
off the ellipse, and passes through the origin again.
What are the coordinates of the point where the ray
first meets the ellipse?

More generally, what if the equation of the ellipse is
x^{2}/a^{2} +
y^{2}/b^{2} = 1?