Q97 / 155 · WBJEE 2025 · Mathematics

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
    $2$
  • Correct answer
    B
    $3$
  • C
    $4$
  • D
    $5$

Solution

$\begin{aligned} & (x-2)^2+(y-3)^2-12-13=0 \\ & (x-2)^2+(y-3)^2=5^2 \\ & (x+3)^2+(y+9)^2=-26+9+81=64 \\ & C_1(2,3) \quad r_1=5 \\ & C_2(-3,-9) \quad r_2=8 \\ & C_1 C_2=\sqrt{25+144}=13 \\ & C_1 C_2=r_1+r_2 \\ & \Rightarrow 3 \text { common tangents. }\end{aligned}$

Hence, the correct answer is option: 'B'.

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