Question

The number of common tangents to the circles \( x^2 + y^2 = 4 \) and \( x^2 + y^2 - 6x - 8y = 24 \) is:

• A. 0
• B. 1
• C. 3
• D. 4

Hint:

To determine the number of common tangents, consider the position and size of the circles.

Answer 1

The Correct Option is B

Step 1: Understand the problem.
The number of common tangents to two circles depends on their relative positions. Here, the circles touch at exactly one point.
Step 2: Conclusion.
Thus, there is exactly one common tangent.
Final Answer: \[ \boxed{1} \]