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

Algebra.Com
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(52802)   (Show Source): You can put this solution on YOUR website!
.

The distance from the center to any foci is  c = ,

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 =  =  =  = 15 meters.     ANSWER

Solved.

-------------

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



RELATED QUESTIONS

Please help me solve this problem. The dome of a whispering gallery has the form of a (answered by CPhill)
A whispering gallery has a semielliptical ceiling that is 12m high and 40m long how high... (answered by ikleyn)
A sound whispered at one focus of a whispering gallery can be heard at the other focus.... (answered by ikleyn)
A whispering gallery has a semielliptical ceiling that is 9 m high and 30 m long. How... (answered by greenestamps)
Hopefully this is the right place for the following story problem. A whispering... (answered by ikleyn)
A domed ceiling is a parabolic surface. For the best lighting on the floor, a light... (answered by lwsshak3)
A domed ceiling is a parabolic surface. For the best lighting on the floor, a light... (answered by lwsshak3)
A domed ceiling is a parabolic surface. FOr the best lighting on the floor, a light... (answered by lwsshak3)
A whispering gallery allows a whisper in one area to be heard plainly in a second area. A (answered by ikleyn)