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Easy Peasy Parabola (Posted on 2018-04-11) Difficulty: 2 of 5
Consider two points A (1,0), and B (5,4) and a parabola y2=4x.

Find coordinates of point P on the parabola for which the sum of PA + PB is minimal.

No Solution Yet Submitted by Danish Ahmed Khan    
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Some Thoughts It really is easy Comment 1 of 1

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
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