JEE Mains · Maths · STD 11 - 10.1 circle and system of circle
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 ________.
- A 6
- B 12
- C 18
- D 24
Answer & Solution
Correct Answer
(C) 18
Step-by-step Solution
Detailed explanation
Let the foot of the perpendicular from the origin to the chord \(AB\) be \(P(h, k)\). The slope of \(OP\) is \(\dfrac{k}{h}\). Since the chord \(AB\) is perpendicular to \(OP\), its equation is given by: \(y - k = -\dfrac{h}{k}(x - h) \Rightarrow hx + ky = h^2 + k^2\) This can…
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