# Perpendicular tricks!

Geometry Level 5

Take a second degree curve $S\equiv b^2x^2 + a^2y^2 -2b^2hx-2a^2ky- a^2b^2+b^2h^2+a^2k^2=0$ Now a line $L\equiv x\cos \alpha + y\sin \alpha - p-h\cos \alpha-k\sin\alpha=0$

intersects the curve $$S=0$$ and the points of interception makes right angle at the centre of the curve. If $$r$$ is the radius of the circle, centred at the centre of $$S$$, that the line $$L=0$$ touches, find $$r^2$$ when $$a=\sqrt5$$ and $$b= \sqrt3$$.

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