Q. For the given circles $x^{2} + y^{2} - 6x - 2y + 1 = 0$and$x^{2} + y^{2} + 2x - 8y + 13 = 0$, which of the following is true?
A) One circles lies inside the other
B) One circle lies completely outside the other
C) Two circles intersect in two points
D) They touch each other externally
Explanation
(d)
The centres of given circles are $C_{1}(3,\ 1)$ and $C_{2}( - 1,\ 4)$ and corresponding radii are
$r_{1} = \sqrt{3^{2} + 1^{2} - 1} = 3$
and $r_{2} = \sqrt{( - 1)^{2} + 4^{2} - 13} = 2$
Now, $C_{1}C_{2} = \sqrt{( - 1 - 3)^{2} + (4 - 1)^{2}} = 5$
$\therefore\ \ C_{1}C_{2} = r_{1} + r_{2}$
Hence, two circles touch externally
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.