math

any sound from one focus of an ellipse reflects off the ellipse directly back to the other focus. This property explains whispering galleries such as Statuary Hall in Washington DC. Imagine a whispering gallery in the shape of a semi-ellipse.
The distance between F and F is 28 meters, and the distance between the centre between F and F, and the semi-ellipse is 5 meters.
Find the distance sound travels as it leaves focus F and returns to focus F'.

a. 30.3 meters
b. 29 meters
c. 59.4 meters
d. 31.4 meters
e. 29.7 meters

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  1. "and the distance between the centre between F and F, and the semi-ellipse is 5 meters. " ---> confusing, but I think I figured it out

    Use the properties of an ellipse in terms of its values of a, b, and c
    c = 14
    b = 5
    a = ??
    In a standard ellipse, a^2 = c^2 + b^2
    a^2 = 14^2 + 5^2 = 221
    a = √221
    distance traveled = 2a
    = 2√221 = appr 29.7 m

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