SOLUTION: A big room is constructed so that the ceiling is a dome that is semielliptical in shape. If a person stands at one focus and speaks, the sound that is made bounces off the ceiling

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Question 1170540: A big room is constructed so that the ceiling is a dome that is semielliptical in shape. If a person stands at one focus and speaks, the sound that is made bounces off the ceiling and gets reflected to the other focus. Thus, if two people stand at the foci (ignoring their heights),they will be able to hear each other. If the room is 34 m long and 8 m high, how far from the center should each of two people stand if they would like to whisper back and forth and hear each other?
Answer by ikleyn(52798) About Me  (Show Source):
You can put this solution on YOUR website!
.

The distance from the center to any foci is  c = sqrt%28a%5E2+-+b%5E2%29,

where "a" and "b" are semi-major and semi-minor axes.


In your case  a = 34/2 = 17 meters;  b = 8 meters.


Therefore,  The distance from the center to any foci is  

    c = sqrt%2817%5E2+-+8%5E2%29 = sqrt%28289+-+64%29 = sqrt%28225%29 = 15 meters.     ANSWER

Solved.

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For more information,  see the lessons
    - Ellipse definition, canonical equation, characteristic points and elements
    - Practical problems from the archive related to ellipses and parabolas
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