Question

The number of common tangents to the circles \[ x^2+y^2-4x-6y-12=0,\quad x^2+y^2+6x+18y+26=0 \] is:

• A. \( 2 \)
• B. \( 3 \)
• C. \( 4 \)
• D. \( 5 \)

Hint:

Common tangents: \begin{itemize} \item \( d > r_1+r_2 \Rightarrow 4 \) \item \( d = r_1+r_2 \Rightarrow 3 \) \item \( |r_1-r_2| < d < r_1+r_2 \Rightarrow 2 \) \end{itemize}

Answer 1

The Correct Option is C