Math Assignment Help With Position Of A Point With Respect To Parabola

7.5.5 Position of a point with respect to parabola

position of a point with respect to parabola

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

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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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