MATHEMATICS · Multi-part · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices
Problem
Let P(x1,y1) be any point on the parabola y2=4ax with focus F(a,0). The point P′(x1,−y1) is the reflection of P in the axis of the parabola.
(i) Prove that the distances PF and P′F are equal.
(ii) Show that the segment PP′ is perpendicular to the axis and that its midpoint lies on the axis.
(iii) Using your results, explain why every pair of reflected points on the parabola are equidistant from the focus.