Consider two points A (1,0), and B (5,4) and a parabola y2
Find coordinates of point P on the parabola for which the sum of PA + PB is minimal.
By inspection, (1,0) is the focus of the parabola, and since 4^2=4*4, (4,4) is a point on the parabola.
Call that point p, for the moment. pB is parallel to the x-axis. Consider a ray of light passing through B to P. By definition it will be focussed at the focus, A. By the principle of least time, this must be the shortest path. So p=P.
Posted by broll
on 2018-04-11 07:58:35