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JEE Mains · Maths · STD 11 - 10.1 circle and system of circle
Consider a circle \(C_1: x^2+y^2-4 x-2 y=\alpha-5\).Let its mirror image in the line \(y=2 x+1\) be another circle \(C _2: 5 x ^2+5 y ^2-10 fx -10 gy +36=0\).Let \(r\) be the radius of \(C _2\). Then \(\alpha+ r\) is equal to \(......\).
- A \(1\)
- B \(2\)
- C \(3\)
- D \(4\)
Answer & Solution
Correct Answer
(B) \(2\)
Step-by-step Solution
Detailed explanation
\(x^2+y^2-4 x-2 y+5-\alpha=0,\) \(C_1(2,1) r_1=\sqrt{\alpha}\) \(2 x-y+1=0\) Image of \((2,1)\) \(\frac{x-2}{2}=\frac{y-1}{-1}=\frac{-2(4-1+1)}{5}\) \(\frac{x-2}{2}=\frac{y-1}{-1}=\frac{-8}{5}\) \(x=2-\frac{16}{5}=\frac{-6}{5}, y=1+\frac{8}{5}=\frac{13}{5}\)…
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