WBJEE · Maths · Circle
The number of common tangents to the circles \(x^2+y^2-4 x-6 y-12=0, x^2+y^2+6 x+18 y+26=0\) is
- A \(2\)
- B \(3\)
- C \(4\)
- D \(5\)
Answer & Solution
Correct Answer
(B) \(3\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & (x-2)^2+(y-3)^2-12-13=0 \\ & (x-2)^2+(y-3)^2=5^2 \\ & (x+3)^2+(y+9)^2=-26+9+81=64 \\ & C_1(2,3) \quad r_1=5 \\ & C_2(-3,-9) \quad r_2=8 \\ & C_1 C_2=\sqrt{25+144}=13 \\ & C_1 C_2=r_1+r_2 \\ & \Rightarrow 3 \text { common tangents. }\end{aligned}\)
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