SOLUTION: As part of an art show, a gallery owner asks a student from a university to design a unique exhibit that will highlight one of the more significant pieces in the collection, an anc

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Question 1187287: As part of an art show, a gallery owner asks a student from a university to design a unique exhibit that will highlight one of the more significant pieces in the collection, an ancient sculpture. The student decides to create an elliptical showroom with reflective wall, with a rotating laser light on a stand at one focus, and the sculpture placed at the other focus on a stand of equal height. The laser light then points continually at the sculpture as it rotates. If the elliptical room is 24 feet long and 16 feet wide, how far from the center of the ellipse should the stands be located (round to the nearest tenth of a foot). How far apart are the stands?
(1) Given
(2) Required to find
(3) Graph/Illustration
(4) Equation to be used
(5) Computation
(6) Final answer
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
(1) Given Major axis =24ft , Minor Axis =16ft
(2) Required to find Focal distance =c, and distance between foci =2c
(3) Graph/Illustration

(4) Equation to be used
a%5E2=b%5E2%2Bc%5E2 where
a=semi-major axis = major axis/2,
b=semi-minor axis = minor axis/2
c=focal distance distance from the center of the ellipse to each focus
(5) Computation
a=24ft%2F2=12ft b=16ft%2F2=8ft
a%5E2=b%5E2%2Bc%5E2 --> c%5E2=a%5E2-b%5E2
c%5E2=%2812ft%29%5E2-%288ft%29%5E2 --> c%5E2=144ft%5E2-64ft%5E2 --> c%5E2=80ft%5E2 --> c=sqrt%28208ft%5E2%29 --> c=8.944ft%29 --> c=highlight%288.9ft%29
2c=2%2A8.944ft --> c=17.888ft 2c=highlight%2817.9ft%29
(6) Final answer
The stands should be located highlight%288.9ft%29 from the center of the room.
The stands will be highlight%2817.9ft%29 apart (rounding the final result, not doubling the rounded value for c).