# JEE Coordinate (3)!

Geometry Level 4

Variable pairs of chords at right angles and drawn through a point $$P$$ (with eccentric angle $$\frac\pi4$$) on the ellipse $$\dfrac{x^2}4+y^2 = 1$$ to meet the ellipse at two points, say $$A$$ and $$B$$.

If the line joining $$A$$ and $$B$$ passes through a fixed point $$Q=(a,b)$$ and the value of $$a^2+b^2$$ can be expressed as $$\dfrac mn$$, where $$m$$ and $$n$$ are coprime positive integers, submit your answer as $$n-m$$.

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