JEE Mains · Maths · STD 11 - 10.1 circle and system of circle
If the curves, \(x^{2}-6 x+y^{2}+8=0\) and \(\mathrm{x}^{2}-8 \mathrm{y}+\mathrm{y}^{2}+16-\mathrm{k}=0,(\mathrm{k}>0)\) touch each other at a point, then the largest value of \(\mathrm{k}\) is
- A \(25\)
- B \(36\)
- C \(30\)
- D \(42\)
Answer & Solution
Correct Answer
(B) \(36\)
Step-by-step Solution
Detailed explanation
Common tangent is \(\mathrm{S}_{1}-\mathrm{S}_{2}=0\) \(\Rightarrow-6 x+8 y-8+k=0\) Use \(\mathrm{p}=\mathrm{r}\) for \(\mathrm{I}^{\text {st }}\) circle \(\Rightarrow \frac{|-18-8+k|}{10}=1\) \(\Rightarrow \mathrm{k}=36\) or \(16 \Rightarrow \mathrm{k}_{\max }=36\)
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