JEE Mains · Maths · STD 11 - 10.1 circle and system of circle
If a variable line, \(3x + 4y -\lambda = 0\) is such that the two circles \(x^2 + y^2 -2x -2y + 1 = 0\) and \(x^2 + y^2 -18x -2y + 78 = 0\) are on its opposite sides, then the set of all values of \(\lambda \) is the interval
- A \((2, 17)\)
- B \([13, 23]\)
- C \([12, 21]\)
- D \((23, 31)\)
Answer & Solution
Correct Answer
(C) \([12, 21]\)
Step-by-step Solution
Detailed explanation
\(3x + 4y - \lambda = 0\) \(\left( {7 - \lambda } \right)\left( {31 - \lambda } \right) < 0\) (since centres lie opposite side) \(\lambda \in \left( {7,13} \right)\,\,\,\,\,\,\,\,\,\,\,.......\left( 1 \right)\) \(\left| {\frac{{7 - \lambda }}{5}} \right| \ge 1\) and…
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