Parabolas and circles BFFs!!

Geometry Level 3

Two points A and B lie on the Parabola y2=4xy^2=4x.

A circle of radius "r" passes through these points such that A and B are ends of its diameter.(AB is a diameter of the circle)

Find the possible values of slopes of AB such that the circle touches the axis of parabola.

Source: IITJEE 2010


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