Q. The number of common tangents to two circles $x^{2} + y^{2} = 4$ and $x^{2} + y^{2} - 8x + 12 = 0$ is
A) 1
B) 2
C) 5
D) 3
Explanation
(d)
The centres and radii of gives circles are $C_{1}(0,\ 0),\ C_{2}(4,\ 0)$ and $r_{1} = 2,\ \ r_{2} = 2$
Now, $C_{1}C_{2} = \sqrt{(4 - 0)^{2} + 0} = 4$
and $r_{1} + r_{2} = 2 + 2 = 4$
$\therefore\ C_{1}C_{2} = r_{1} + r_{2}$
Hence, three common tangents are possible
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.