SOLUTION: 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 b
Algebra ->
Quadratic-relations-and-conic-sections
-> SOLUTION: 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 b
Log On
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? Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website! 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?
***
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
(