a parabolic tv antenna is 18 feet across and 8 feet deep if the receiver is placed at the focus how far is it from the vertex?
let the vertex be at the origin.
the points $\displaystyle (-9,8)$ , $\displaystyle (0,0)$ , and $\displaystyle (9,8)$ are on the parabola.
$\displaystyle y = kx^2$
$\displaystyle 8 = k(9)^2$
$\displaystyle k = \frac{8}{81}$
$\displaystyle y = \frac{8}{81} x^2$
general parabola equation w/ vertex at the origin ...
$\displaystyle y = \frac{x^2}{4p}$
equating ...
$\displaystyle 4p = \frac{81}{8}$
$\displaystyle p = \frac{81}{32}$
find the focal point.