Whispering Gallery: A hall feet in length is to be designed as a whispering gallery. If the foci are located feet from the center, how high will the ceiling be at the center?
The height of the ceiling at the center of the gallery is .
The center of the ellipse be the origin and the major axis be along the x-axis.
Here, the center of the room is at , It is given that the length of the room is .
The distance from the center of the room to each vertex is
The distance from center to each focus is
Substitute and in we get.
Thus, the height of the ceiling at the center of the gallery is feet.
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