1 A person in a whispering gallery standing at one focus of

1) A person in a whispering gallery standing at one focus of the ellipse can whisper and be heard by a person standing at the other focus because all the sound waves that reach the ceiling are reflected to the other person. If a whispering gallery has a length of 170 meters, and the foci are located 13 meters from the center, find the height of the ceiling at the center.

Height:????

2) a)Whats the focal diameter of -8.72x=y^2

2) b) Whats the focal diameter of -34.4x=y^2

Solution

gallery length = 170 metres

major axis 2a = 170

a = 170 / 2

a = 85

foci of ellipse is c^2 = a^2- b^2

13^2 = a^2 - b^2

b^2 = 85^2 - 13^2

b^2 = 7056

therefore height of ceiling is 84 metres