Let be any point on the parabola and let be its reflection in the axis of the parabola

MATHEMATICS · Subjective · CBSE · Mathematics · Conic Sections · Conic Sections

Problem

Let P(x0,y0)P(x_0,y_0) be any point on the parabola y2=4axy^{2}=4ax and let P′(x0,−y0)P'(x_0,-y_0) be its reflection in the axis of the parabola. If F(a,0)F(a,0) is the focus, prove that PF=P′FPF = P'F.

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