SOLUTION: Parabola The antenna of a radio telescope is paraboloid measuring 81 feet across with depth of 16 feet. Determine, to the nearest tenth of a foot, the distance from the vertex t

If you read the lesson

    - Parabola definition, canonical equation, characteristic points and elements 

in this site, you will learn that if you write the canonical equation of a parabola in the form

y = ,     (1)


then the distance from the parabola's vertex (0,0) to the parabola's focus  (focal distance) is  .


So, our nearest task is to present the equation of our parabola in the form (1).

For it, substitute y = 16 (depth in feet)  and  x =   into equation (1). You will get then

16 = ,   or  2p =  = .


Then  p =  = 51.258.


Thus the focal distance is   =  = 25.629 ft.