need help with this math world problem

Question

A satellite dish is in the shape of a paraboloid. Cross sections taken parallel to the direction the dish opens are parabolic. Cross sections taken perpendicular to the direction the dish opens are circular. The diameter of the dish is 30 in. and the depth is 3 in.

1. Find an equation of a parabolic cross section through the vertex of the dish.
2. Where should the receiver be placed?

Answer 1

The standard form of a parabola is(y-k)2=4p(x-h) where (h,k) is the vertex and p is the distance from the vertex to the focus. Assume the vertex is at the origin making h=k=0 and the parabola opens in the positive x direction. Use the given diameter of 30 making y at x=3 to be 30/2=15. Substitute these values into the standard equation and solve for p=18.75 making the focus at (0,18.75). Place the receiver at the focus.