AP EAMCET · Maths · Circle
If the equation of the circle having the common chord to the circles \(x^2+y^2+x-3 y-10=0\) and \(x^2+y^2+2 x-y-20=0\) as its diameter is \(\mathrm{x}^2+\mathrm{y}^2+\alpha \mathrm{x}+\beta \mathrm{y}+\gamma=0\), then \(\alpha+2 \beta+\gamma=\)
- A \(0\)
- B \(1\)
- C \(-1\)
- D \(2\)
Answer & Solution
Correct Answer
(A) \(0\)
Step-by-step Solution
Detailed explanation
Equation of common chord: \( (x^2+y^2+x-3y-10) - (x^2+y^2+2x-y-20) = 0 \) \( -x-2y+10 = 0 \Rightarrow x+2y-10=0 \) Equation of circle passing through intersection: \( S_1 + \lambda L = 0 \) \( x^2+y^2+x-3y-10 + \lambda(x+2y-10) = 0 \)…
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