Q. The equation of the common tangent of the two touching circles, $y^{2} + x^{2} - 6x - 12y + 37 = 0$ and $x^{2} + y^{2} - 6y + 7 = 0$ is
A) $x + y - 5 = 0$
B) $x - y + 5 = 0$
C) $x - y - 5 = 0$
D) $x + y + 5 = 0$
Explanation
(c)
Let $S_{1} \equiv x^{2} + y^{2} - 6x - 12y + 37 = 0$
and $S_{2} \equiv x^{2} + y^{2} - 6y + 7 = 0$
the equation of common tangent of the two circles is $S_{1} - S_{2} = 0$
$\Rightarrow \ \ \ x^{2} + y^{2} - 6x - 12y + 37 - \left( x^{2} + y^{2} - 6y + 7 \right) = 0$
$\Rightarrow \ \ x - y - 5 = 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.