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

7.5.5 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

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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