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?

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
Step 1 Given, The shape of whispering gallery is an ellipse of notation. Step 2 The center of gallery is

Step 3 So, Therefore,

${b}^{2}=1875$
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.