Circles · Locus of intersection of chords

Let the circle

x^2 + y^2 = 4

intersect

x

-axis at the points

A(a, 0)

a > 0

and

B(b, 0)

. Let

P(2\cos\alpha, 2\sin\alpha)

0 < \alpha < \dfrac{\pi}{2}

and

Q(2\cos\beta, 2\sin\beta)

be two points such that

(\alpha - \beta) = \dfrac{\pi}{2}

. Then the point of intersection of

AQ

and

BP

lies on :

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