Question

​You are given a positive number p, but you are not told what the specific value of p is. A vertical light beam comes from high above the plot of f[x] = x^2/(4 p) and bounces off the curve at a given point point {a, f[a]}. You are not told what the specific value of a is. Calculate in terms of p the point at which the reflected beam crosses the y-axis.​

Answer 1

(x, y) = (0, p)

Explanation:

In the given equation, p is the distance from the vertex (0, 0) to the focus of the parabola. Any vertical "light beam" will bounce off the curve and pass through the focus at (0, p).