Word problem involving comic sections. A hall 100 feet in length is designed as a whispering gallery (See example 9 for Ellipses). If the focus is 25 feet from the center, how high will the ceiling be at the center?

sibuzwaW 2021-01-10 Answered
Word problem involving comic sections. A hall 100 feet in length is designed as a whispering gallery (See example 9 for Ellipses). If the focus is 25 feet from the center, how high will the ceiling be at the center?
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Dora
Answered 2021-01-11 Author has 98 answers
Step 1 Given, The shape of whispering gallery is an ellipse of notation. Step 2 The center of gallery is (0, 0).
Foci =(± 25, 0)
Vertices=(± 50, 0) Step 3 So, a=50 and c=25 Therefore, c2=a2  b2
252=502  b2
b2=502  252
b2=2500  625
b2=1875
b 43.30 Step 4 Here b is length of minor axis, which is height of ceiling. So, the height of ceiling is equal to 43.3 feet.
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