SOLUTION: A whispering gallery has a semielliptical ceiling that is 12m high and 40m long how high is the ceiling above the two foci?

From the condition, the major semi-axis of the ellipse has the length of a = 20 m.

The length of the minor semi-axis is b = 12 m.

The linear eccentricity is c =  =  =  =  = 16.


So the foci are located on the major axis (which is the horizontal line at the floor) 

at the distance of 16 m from the center point.


Taking the center point as the origin of the coordinate system,
the standard equation of the ellipse is 

 +  = 1.              (1)


Then y = +/- .     (2)


To calculate the elevation at the focus, we must substitute x = 16 into the formula (2) and calculate y:

y =  =  =  =  = 7.2 m.


Answer.  The ceiling above the two foci is at 7.2 m.