Explanation/(answer)

Question

In a room shaped like an ellipse, something whispered at 1 focus can be clearly heard at the other focus. The US Capitol National Statuary Hall in Washington, DC is such a whispering gallery. If the elliptical pattern of this whispering gallery is 92 feet long by 58 feet wide, how far from the whisperer at 1 focus is the listener at the other focus?

Answer 1

From the description of the problem, the length of the major axis is 2a = 92

……> a= 46

The length of the minor axis is 2b = 58

…….> b = 29

Treating the center of the ellipse at the origin,

then each focus is at a distance c = √ (a² - b²) from the origin.

The distance between the two foci is therefore 2c = 10√51

Do the calculations.

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Hilton Tottaram