JEE Mains · Maths · STD 11 - 10.1 circle and system of circle
The diameter of the circle, whose centre lies on the line \(x+y=2\) in the first quadrant and which touches both the lines \(x=3\) and \(y=2,\) is
- A \(12\)
- B \(9\)
- C \(3\)
- D \(6\)
Answer & Solution
Correct Answer
(C) \(3\)
Step-by-step Solution
Detailed explanation
\(\because\) center lies on \(x+y=2\) and in 1 st quadrant center \(=(\alpha, 2-\alpha)\) where \(\alpha>0\) and \(2-\alpha>0 \Rightarrow 0<\alpha<2\) \(\because\) circle touches \(x=3\) and \(y=2\) \(\Rightarrow \quad|3-\alpha|=|2-(2-\alpha)|=\) radius…
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