Prove that the light ray sent from one focus of ellipse mirror end up in another

I have trouble proving the following problem from Zorich Mathematical Analysis I

So we have previously reached that the equation for the tangent line through $(x_0,y_0)$，we have the equation of the tangent line as $$\frac{xx_0}{a^2}+\frac{yy_0}{b^2}=1$$