Question

a hall 100 feet in length is to be designed as a whispering gallery. If the foci are located 25 feet from the​ center, how high will the ceiling be at the​ center?

Answer 1

Answer:

how high will the ceiling be at the center? ≈43.3 ft above the center

Step-by-step explanation:

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

≈43.3 ft above the center