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

6 bx ay tan a and tan B 1 Y The slope of F Pis I1 c So a 3 Y1 x1 c 2x bcx a c ...

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 α and β be the angles between the lines PF1, PF2 and the ellipse as in the figure. Prove that α = β. This explains how whispering galleries and lithotripsy work. Sound coming from one focus is reflected and passes through the other focus.