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Variable pairs of chords at right angles...

Variable pairs of chords at right angles and drawn through any point P (with eccentric angle `pi/4`) on the ellipse `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) such that `a^2 + b^2` has the value equal to `m/n` where m, n are relatively prime positive integers, find `(m + n)`.

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