Let P(x1, y1) be a point on the ellipse x2/a2 + y2/b2 = 1 with foci F1

Question:

Let P(x1, y1) be a point on the ellipse x2/a2 + y2/b2 = 1 with foci F1 and F2 and let a and ( be the angles between the lines PF1, PF2 and the ellipse as shown in the figure. Prove that a = (. This explains how whispering galleries and lithotripsy work. Sound coming from one focus is reflected and passes through the other focus.