Q. The number of common tangents to the circles $x^{2} + y^{2} = 4$ and $x^{2} + y^{2} - 6x - 8y + 24 = 0$ is
A) 3
B) 4
C) 2
D) 1
Explanation
(b)
The centre and radii of circles are $C_{1}(0,\ 0),\ C_{2}(3,\ 4)$ and
$r_{1} = 2,\ r_{2} = \sqrt{9 + 16 - 24} = 1$
Now, $C_{1}C_{2} = \sqrt{(3 - 0)^{2} + (4 - 0)^{2}} = 5$
$r_{1} + r_{2} = 2 + 1 = 3$
Since, $C_{1}C_{2} > r_{1} + r_{2}$
$\therefore$ Number of common tangents=4
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.