SOLUTION: The ceiling of a whispering gallery is in semi-elliptical in shape. Two people at the foci can hear each other whisper, since sound from any focus bounces off the ceiling to the ot

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: The ceiling of a whispering gallery is in semi-elliptical in shape. Two people at the foci can hear each other whisper, since sound from any focus bounces off the ceiling to the ot      Log On


   

Question 1183608: The ceiling of a whispering gallery is in semi-elliptical in shape. Two people at the foci can hear each other whisper, since sound from any focus bounces off the ceiling to the other focus. If the gallery is 46 ft across and 15 ft high at the center, how far apart are the two points where two people should stand so they can hear each other whisper?
Answer by ikleyn(52790) About Me  (Show Source):
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The ceiling of a whispering gallery is in semi-elliptical in shape. Two people at the foci can hear each other whisper,
since sound from any focus bounces off the ceiling to the other focus. If the gallery is 46 ft across and 15 ft high at the center,
how far apart are the two points where two people should stand so they can hear each other whisper?
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The major semi-axis of the ellipse is  a = 46/2 = 23 feet.


The minor semi-axis is b = 15 feet.


The distance between the focuses of the ellipse is twice the linear eccentricity


    d = 2%2Asqrt%28a%5E2-b%5E2%29 = 2%2Asqrt%2823%5E2+-+15%5E2%29 = 2%2Asqrt%28304%29 = 34.87 ft.      ANSWER

Solved.

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On ellipses, read from the lessons
    - Ellipse definition, canonical equation, characteristic points and elements
    - Ellipse focal property
    - Tangent lines and normal vectors to an ellipse
    - Optical property of an ellipse
in this site.