Through the vertex of the parabola \(y^2 = 4ax\), two chords are drawn and the circle on these chords as diameters intersect at a point.

If \(A\) and \(B\) be the angles made with the \(x\)-axis by tangents at the other ends of chords and \(C\) be the angle made with the \(x\)-axis by the line joining vertex of the parabola and point of intersection of circles, then \(\cot(A)+\cot(B)+m\tan(C) = 0\) for some constant positive integer \(m\).

Find \(m\).

This is a part of my set Practice for JEE 2017!

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