You solve the 2 equations simultaneously.

From parabola you get: 8y = x^{2}

From eqn of chord: 8y = 2(8-3x) = 16-6x

.: x^{2}= 16 - 6x ==> x^{2}+ 6x -16= 0 ==> (x+8)(x-2) = 0

So chord intersects parabola at x = -2 as well. x=2 ==> y = (8-3x)/4 = (8 - 3*2)/4 = 1/2 = 2

So Q has co-ords (2,1/2)

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