# Math Help - parabolic tv antenna ( HELP!!! )

1. ## parabolic tv antenna ( HELP!!! )

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?

2. Originally Posted by ddo
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 $(-9,8)$ , $(0,0)$ , and $(9,8)$ are on the parabola.

$y = kx^2$

$8 = k(9)^2$

$k = \frac{8}{81}$

$y = \frac{8}{81} x^2$

general parabola equation w/ vertex at the origin ...

$y = \frac{x^2}{4p}$

equating ...

$4p = \frac{81}{8}$

$p = \frac{81}{32}$

find the focal point.