The equation of the circle touching the circle $x^2+y^2-6 x+$ $6 y+17=0$ externally and to which the lines $x^2-3 x y-3 x$ $+9 y=0$ are normal is

• A

  $x^2+y^2-3 x+2 y-2=0$
• Correct answer
  B

  $x^2+y^2-6 x-2 y+1=0$
• C

  $x^2+y^2+6 x-2 y-1=0$
• D

  $x^2+y^2-9 x-3 y+2=0$

Solution

$x^2-3 x y-3 x+9 y=0$ $\Rightarrow(x-3)(x-3 y)=0 \Rightarrow x=3, y=1$
Centre of required circle $=(3,1)$ $r_1+r_2=4 \Rightarrow r_1=1 \Rightarrow r_2=3$
Equation of the required line is $\begin{aligned} & (x-3)^2+(y-1)^2=9 \\ & \Rightarrow x^2+y^2-6 x-2 y+1=0 \end{aligned}$

Hence, the correct answer is option: 'B'.