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?

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- May 18th 2010, 03:48 PMddoparabolic 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?** - May 18th 2010, 04:46 PMskeeter
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.