Question

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

Answer 1

Answer: (B)

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 $S_1-S_2=0$
$\Rightarrow x^2+y^2-6x-12y+37$
$-\left(x^2+y^2-6y+7\right)=0$
$\Rightarrow -6x+6y+30=0$
$\Rightarrow x-y-5=0$