SOLUTION: A designer of a 200-foot-diameter parabolic electromagnetic antenna for tracking space probes wants to place the focus 100 feet above the vertex. Find the equation of the parabola

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Question 742955: A designer of a 200-foot-diameter parabolic electromagnetic antenna for tracking space probes wants to place the focus 100 feet above the vertex. Find the equation of the parabola using the axis of the parabola as the y-axis and vertex as the origin then determine the depth of the parabolic reflector.
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Textbook derivation should show a result of a basic parabola as 4py=x%5E2, where p is the distance from vertex to focus. Your example uses p=100, so you have a parabola describing 4%2A100%2Ay=x%5E2, or highlight%28y=%281%2F400%29x%5E2%29.

The diameter of the antenna being 200 feet means that radius is 100 feet. The is in the x direction. To find how deep, use x=100 in the parabola's equation to find y, which will be how deep. Depth=y=%281%2F400%29%28100%29%5E2, depth is 25 feet.