Find the locus of the point through which pass three normals to the parabola

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

Problem

Find the locus of the point through which pass three normals to the parabola y2=4axy^2=4ax, such that two of them make angles α\alpha and β\beta, respectively, with the axis and tan⁡αtan⁡β=2\tan\alpha\tan\beta=2.

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