The tangents to the parabola at and intersect at

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

Problem

The tangents to the parabola y2=4axy^2=4ax at P(at12,2at1)P(at_1^2,2at_1) and Q(at22,2at2)Q(at_2^2,2at_2) intersect at RR. Prove that the area of △PQR\triangle PQR is 12a2∣t1−t2∣3\frac{1}{2}a^2|t_1-t_2|^3.

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