SOLUTION: A giant parabolic dish has a diameter of 400 meters and a depth of 80 meters. find an equation in the form that describes a cross section of this dish. if the receiver is located

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Question 1037089: A giant parabolic dish has a diameter of 400 meters and a depth of 80 meters. find an equation in the form that describes a cross section of this dish.
if the receiver is located at the focus, how far should it be from the vertex?

Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Cross section is a parabola shape. Imagine the vertex at the Origin, and this vertex as a minimum.

Radius is half of the diameter, being radius of 200. "Depth" becomes there distance of 80 meters. This is a cartesian point, (200,80). Standard Form can start as y=a%28x-0%29%5E2%2B0, the two 0 values because the vertex is (0,0), the Origin as picked here. This more simply is y=ax%5E2.

Use the point on the rim of the cross section to find coefficient, a.
a=y%2Fx%5E2
a=80%2F200%5E2
a=80%2F40000
a=2%2F1000
a=1%2F500
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Finished equation for the cross section is highlight%28y=%281%2F500%29x%5E2%29.

You can find the focus using this video presentation's information as help:
Deriving Equation for Parabola using given Focus and Directrix