Problem

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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