A parabolic dish is 18 inches across and 2 inches deep Find

A parabolic dish is 18 inches across and 2 inches deep. Find its focal length

Solution

A parabola with vertex (0,0)is given as with y axis as axis of symmetry:

x^2 = 4py

where ( 0, p) is the focus

Plug the outer point of the cross-section is (9, 1), and this point will satisfy the equation

(9)^2 = 4*p*1

p = 81/4

Focal length is 81/4 inches