An engineer designs a satellite dish with a parabolic cross section. The dish is 14 ft wide at the​ opening, and the focus is placed 4 ft from the vertex.

Question

​a) Position a coordinate system with the origin
at the vertex and the​ x-axis on the​ parabola's
axis of symmetry and find an equation of the
parabola.

​b) Find the depth of the satellite dish at the vertex.

Answer 1

the general equation is
... x = a(y - k)^2 + h

the vertex is at the origin, so h and k are both zero

a = 1 / 4p
... where p is the distance from the vertex to the focus

b) the center depth is the value of x at the edges of the dish (where y equals ±7)