The number of common tangents to the circles $x^2 + y^2 - 4x - 6y - 12 = 0$ and $x^2 + y^2 + 6x + 18y + 26 = 0$ is:
Step-by-Step Solution
Key Concept: $C_1 = (2, 3)$, $r_1 = 5$; $C_2 = (-3, -9)$, $r_2 = 8$. Distance $d = \sqrt{5^2 + 12^2} = 13 = r_1 + r_2$. External tangency $\Rightarrow$ exactly $3$ common tangents.
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Correct Answer: (3)