Question:medium
Consider the circle \(C: x^2 + y^2 - 6x - 8y - 11 = 0\). Let a variable chord AB of the circle \(C\) subtend a right angle at the origin. If the locus of the foot of the perpendicular drawn from the origin on the chord AB is the circle \(x^2 + y^2 - \alpha x - \beta y - \gamma = 0\), then \(\alpha + \beta + 2\gamma\) is equal to ________.
Consider the circle \(C: x^2 + y^2 - 6x - 8y - 11 = 0\). Let a variable chord AB of the circle \(C\) subtend a right angle at the origin. If the locus of the foot of the perpendicular drawn from the origin on the chord AB is the circle \(x^2 + y^2 - \alpha x - \beta y - \gamma = 0\), then \(\alpha + \beta + 2\gamma\) is equal to ________.
Updated On: Apr 12, 2026
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Correct Answer: 18
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