Let be a point on the ellipse with foci and and let and be the angles between the lines

Chapter 10, Problem 65

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Let be a point on the ellipse with foci and and let and be the angles between the lines and the ellipse as shown in the figure. Prove that . This explains how whispering galleries and litho tripsy work. Sound coming from one focus is reflected and passes through the other focus. [Hint: Use the formula in on page 195 to show that .]

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