Prove that the area of the triangle inscribed in the parabola is 1 8a…

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

Problem

Prove that the area of the triangle inscribed in the parabola y2=4axy^2=4ax is 18a∣(y1−y2)(y2−y3)(y3−y1)∣,\frac{1}{8a}\left|(y_1-y_2)(y_2-y_3)(y_3-y_1)\right|, where y1y_1, y2y_2, and y3y_3 are the ordinates of the vertices.

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