Equation for Parabola with Given Focus and Width: Homework Problem

[pythagman]

Homework Statement

A parabolic communications antenna has a focus 6 feet above its vertex. Write an equation for the parabola and find the width of the antenna 9 feet from the vertex. Locate the origin strategically.

Homework Equations

y= x^2 (parent equation for parabola)

The Attempt at a Solution

focus = 4p.
standard form of parabola , (x-h)^2 = 4p(y-k)^2
4 * 6 = 24 so (x-h)^2 = 24(y-k)^2.
It doesn't give you the origin how are you supposed to write the formula?

 

[Dick]

(h,k) is the vertex. You can put the origin anywhere you like. Why not put it at the vertex? So (h,k)=(0,0). Now what's the y coordinate 9 feet from the vertex? BTW, check your standard form for a parabola. You've got an extra square in there.

 

[sdykikyou]

Hello...

You've got an extra square in there.

I believe you're right. The equation is (x-h) = 4p(y-k)^2

or (y-k) = 4p(x-h)^2

So, just try x = 24y^2 and work from there ^^