Question

The locus of the centre of a circle, which touches externally the circle $x^2+y^2-6x-6y+14=0$ and also touches the y-axis, is given by the equation

• A. $x^2-6x-10y+14=0$
• B. $x^2-10x-6y+14=0$
• C. $y^2-6x-10y+14=0$
• D. $y^2-10x-6y+14=0$

Answer 1

The correct option is D $y^2-10x-6y+14=0$

The circle $x^2+y^2-6x-6y+14=0$ is given
Centre $C_1(3,3)$ and radius $=2$


Let the centre of another circle is $C_2(h,k)$ which is touching at $y-$axis so radius is $h$.
So, $C_1{C}_2=h+2$
$\Rightarrow \sqrt{(3-h{)}^2+(3-k{)}^2}=h+2$
$\Rightarrow k^2-10h-6k+14=0$
$\Rightarrow y^2-10x-6y+14=0$