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MathsJEE Main 8 Apr 2026, Shift 2·Q24·Numerical·Tough

Circles · Locus by homogenisation of chord

Consider the circle C:x2+y2−6x−8y−11=0C : x^2 + y^2 - 6x - 8y - 11 = 0. Let a variable chord ABAB of the circle CC subtend a right angle at the origin. If the locus of the foot of the perpendicular drawn from the origin on the chord ABAB is the circle x2+y2−αx−βy−γ=0x^2 + y^2 - \alpha x - \beta y - \gamma = 0, then α+β+2γ\alpha + \beta + 2\gamma is equal to .

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