Chord of circle C2 (Jee Mains)

Chords & Intersection of Circles

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Chord of circle C2

Let y = x be the equation of a chord of the circle C₁ (in the closed half-plane x ≥ 0) of diameter 10 passing through the origin. Let C₂ be another circle described on the given chord as its diameter. If the equation of the chord of the circle C₂, which passes through the point (2, 3) and is farthest from the center of C₂, is x + ay + b = 0, then a – b is equal to :

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