Question

A ray of light emerging from the point p(0, 4) along the tangent of the ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$ and strike a circle of radius $\sqrt{65}$ units and reflected from it. The reflected ray entering inside the ellipse through the focus (-3, 0) and strike lower surface of ellipse and gets reflected from it. If the reflected ray returns to the point p (0, 4), then ordinate of the center of circle is ______

Answer 1

2

Answer 2

The ray leaves the point P = (0,4) along the horizontal tangent to the ellipse. Writing the circle (x–h)²+(y–k)²=65 with R = (x_R, 4) (on y = 4) and applying the law of reflection at R shows that the reflected ray passes through F = (–3, 0). Then, using the additional reflection on the ellipse and imposing the condition that the final reflected ray returns to P leads (after algebra) to the unique possibility k = 2.