Math help!! Algebra 1 or 2

Question

The cross section of television antenna dish is a parabola and the receiver is located at the focus, 5 feet above the vertex.

A. find an equation for the cross section of the dish.( assume the vertex is at the origin.)

b. If the television antenna is 10 feet wide how deep is it?

Answer 1

x² = 4py where the focus is at the point (0,p)

Focus at (0,5) so x² = 4(5)y, or y = x²/20 the width is 10 ft, therefore, a point on the parabola must be (5,y)

y = 25/20, or y = 1.25 feet, or 1 foot, 3 inches or 15 inches.