Q. For the two circles $x^{2} + y^{2} = 16$ and $x^{2} + y^{2} - 2y = 0$ there is/are
A) One pair of common tangents
B) Only one common tangent
C) Three common tangents
D) No common tangent
Explanation
(d)
The centres and radii of given circles are $C_{1}(0,\ 0),\ r_{1} = 4$ and $C_{2}(0,\ 1),$
$\ r_{2} = \sqrt{0 + 1} = 1$
Now, $C_{1}C_{2} = \sqrt{0 + (0 - 1)^{2}} = 1$
and $r_{1} - r_{2} = 4 - 1 = 3\ \ \ \therefore\ \ C_{1}C_{2} < r_{1} - r_{2}$
Hence second circle lies inside the first circle, so no common tangent is possible
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.