Thread: ellipse problem

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 ceiing be at th center?


I believe that the minor axis, 2a is 150 feet and what Im trying to find is the major axis, 2b. So all i have to do is use this equation b2=a2-c2. b2= 75 squared - c2.

I have no idea what c is, or am i doing this completely wrong?

Originally Posted by blackandwhite

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 ceiing be at th center?

If the foci are twenty-five feet from the center, then c = 25. You are given that the room will be 100 feet long, so the ends (the vertices) are clearly fifty feet from the center, so a = 50.

Use the formula relating a, b, and c, to find the value of b. Then write the equation, centering the ellipse (for convenience) at the origin, so (h, k) = (0, 0).