Question 865420
A hall 100 feet in length is to be designed as a whispering gallery ( a hall with elliptical ceiling). If the foci are located 25 feet from the center, how high will the ceiling be at center?
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standard form of equation for an ellipse with horizontal major axis and center at the origin:
x^2/a^2+y^2/b^2=1, a>b
for given problem:
a=50
a^2=2500
c=25
c^2=625
c^2=a^2-b^2
b^2=a^2-c^2=2500-625=1875
b=√1875≈43.3 ft
how high will the ceiling be at center? ≈43.3 ft above center