College Algebra, Chapter 8, 8.1, Section 8.1, Problem 54

Suppose that a reflector for a satellite dish has cross section in parabolic form, with a receiver at focus $F$. The reflector is $1$ ft deep and $20$ ft wide from rim to rim. How far is the receiver from the vertex of the parabolic reflector.

"Please see figure"

If we let the vertex of the parabola lies on the origin and midway between $20$ ft span then its equation is $x^2 = 4py$ where the focus is located at $(0, p)$ and endpoints at $(10,1)$ and $(-10, 1)$. Hence, the endpoints are the solution of the equation, so


$
\begin{equation}
\begin{aligned}

x^2 =& 4py
\\
\\
(10)^2 =& 4p(1)
\\
\\
100 =& 4p
\\
\\
p =& 25

\end{aligned}
\end{equation}
$


Therefore, the receiver is $25$ ft from the vertex of the parabolic reflector.