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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