Show that the line touches the parabola if

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

Problem

Show that the line xcos⁡α+ysin⁡α=px\cos\alpha+y\sin\alpha=p touches the parabola y2=4axy^2=4ax if pcos⁡α+asin⁡2α=0p\cos\alpha+a\sin^2\alpha=0, and that the point of contact is (atan⁡2α,−2atan⁡α)(a\tan^2\alpha,-2a\tan\alpha).

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