Let a parabola with equation
y2 = 4ax
and P(x1, y1) be a point in the plane.
PR is perpendicular to OX meeting parabola at point Q. co-ordinates of point Q are (x2, y2).
Since, point Q lies on y2 = 4ax
Hence,
y22 = 4ax
PR>QR, PR = QR or PR<QR
i.e.
PR2>QR2, PR2 = QR2 or PR2<QR2
i.e.
y12 > y22, y12 = y22 or y12 < y22
y12 > 4ax1, y12 = 4ax1 or y12 < 4ax1 respectively.
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