JEE Mains · Maths · STD 11 - 10.1 circle and system of circle
The set of all real values of \(\lambda \) for which exactly two common tangents can be drawn to the circles \(x^2 + y^2 - 4x - 4y+ 6\, = 0\) and \(x^2 + y^2 - 10x - 10y + \lambda \, = 0\) is the interval:
- A \((12, 32)\)
- B \((18, 42)\)
- C \((12, 24)\)
- D \((18, 48)\)
Answer & Solution
Correct Answer
(B) \((18, 42)\)
Step-by-step Solution
Detailed explanation
The equation of the circles are \({x^2} + {y^2} - 10x - 10y + \lambda = 0\,\,\,\,\,\,\,......\left( 1 \right)\) and \({x^2} + {y^2} - 4x - 4y + 6 = 0\,\,\,\,\,\,\,......\left( 2 \right)\) \({C_1} = \,\) center of \(\left( 1 \right) = \left( {5,5} \right)\) \({C_2} = \,\) center…
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