TS EAMCET · Maths · Circle
If the centre \((\alpha, \beta)\) of a circle cutting the circles \(x^2+y^2-2 y-3=0\) and \(x^2+y^2+4 x+3=0\) orthogonally lies on the line \(2 x-3 y+4=0\), then \(2 \alpha+\beta=\)
- A \(3\)
- B \(-3\)
- C \(0\)
- D \(1\)
Answer & Solution
Correct Answer
(B) \(-3\)
Step-by-step Solution
Detailed explanation
Let the equation of the circle be \(x^2+y^2-2\alpha x-2\beta y+c=0\). Orthogonality with \(x^2+y^2-2 y-3=0\): \(2(-\alpha)(0) + 2(-\beta)(-1) = c + (-3) \implies 2\beta = c - 3\). Orthogonality with \(x^2+y^2+4 x+3=0\):…
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