JEE Mains · Maths · STD 11 - 10.1 circle and system of circle
Let the mirror image of a circle \(c_{1}: x^{2}+y^{2}-2 x-\) \(6 y+\alpha=0\) in line \(y=x+1\) be \(c_{2}: 5 x^{2}+5 y^{2}+10 g x\) \(+10 f y +38=0\). If \(r\) is the radius of circle \(c _{2}\), then \(\alpha+6 r^{2}\) is equal to\(.....\)
- A \(13\)
- B \(11\)
- C \(12\)
- D \(10\)
Answer & Solution
Correct Answer
(C) \(12\)
Step-by-step Solution
Detailed explanation
Image of centre \(c _{1} \equiv(1,3)\) in \(x - y +1=0\) is given by \(\frac{x_{1}-1}{1}=\frac{y_{1}-3}{-1}=\frac{-2(1-3+1)}{1^{2}+1^{2}}\) \(x_{1}=2, y_{1}=2\) \(\therefore\) Centre of circle \(c _{2} \equiv(2,2)\) \(\therefore\) Equation of \(c_{2}\) be…
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