Question

The number of common tangents to the circles $x^2+y^2=4$ and $x^2+y^2-8x+12=0$ is:

• A. 1
• B. 2
• C. 3
• D. 4
• E. none of these

Answer 1

Answer: (C)

The centre and radius of circle $x^2+y^2=4$ are $C_1(0,0)$ and $r_1=2$ respectively and the centre and radius of circle $x^2+y^2-8x+12=0$ are $(4,0)$ and $r_2=2$ . $\because$ $C_1{C}_2=r_1+r_2$ $\therefore$ Circles touch each other externally, therefore number of common tangents are 3.