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an engineer designs a satellite dish with a parabolic cross section. The dish is 15 ft wide at the opening and the focus is placed 4 ft from the vertex. find an equation of the parabola.

I know how to work this problem, but how do I know that I use the equation y^2 = 4px instead of x^2 = 4py.

You cannot solve it, without knowing someting more. Is the 15ft width measured in relation to the vertex somehow? There has to be more than the width, it must also containg some measure of depth of the dish.

Aside from giving a little more info, it doesn't matter which equation you use. That just assigns the variables. Use which feels more comfortable. I'd probably use 4py = x^2.

p is the distance from the vertex to the focus, so

4(4)y = x^2
y = x^2/16

Now for that pesky 15' diameter:
If we want to find how deep the dish is, then y(7.5) = 56.25/16 = 3.5'

Seems the focus is mounted higher than the rim of the dish.

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