Answer
(a) $y=\frac{3}{500}x^2$
(b) 41.7 ft
Work Step by Step
(a) 1. Assume the equation is $x^2=4py$
2. As point $(50,15)$ is on the curve, we have $50^2=4p(15)$, thus $p=\frac{500}{12}$
3. Thus the equation is $x^2=\frac{500}{3}$ or $y=\frac{3}{500}x^2$
(b) The focus can be found at $(0,p)$, thus the receiver should be at $(0,\frac{500}{12})$ or $(0,41.7)$ or about 41.7 ft from the vertex.
