COMEDK · Maths · 12. Circle
The number of common tangents to the circles \(x^{2}+y^{2}-2 x-4 y+1=0\) and \(x^{2}+y^{2}-12 x-16 y+91=0\) is
- A 1
- B 2
- C 3
- D 4
Answer & Solution
Correct Answer
(D) 4
Step-by-step Solution
Detailed explanation
We have, \[ x^{2}+y^{2}-2 x-4 y+1=0 \] and \(x^{2}+y^{2}-12 x-16 y+91=0\) Here, \(\quad C_{1} \equiv(1,2)\) and \(r_{1}=\sqrt{1+4-1}=2\) and \(\quad C_{2} \equiv(6,8)\) and \(r_{2}=\sqrt{36+64-91}=3\) Now, \(C_{1} C_{2}=\sqrt{25+36}=\sqrt{61}\) Here,…
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