Question

The equation of a circle of radius 1 touching the circles $x^2+y^2-2|x|=0$ is

• A. $x^2+y^2+2\sqrt{3}x-2=0$
• B. $x^2+y^2-2\sqrt{3}y-2=0$
• C. $x^2+y^2+2\sqrt{3}y+2=0$
• D. $x^2+y^2+2\sqrt{3}x+2=0$

Answer 1

The correct option is C

$x^2+y^2+2\sqrt{3}y+2=0$

Required circle centre lies on y-axis i.e(0, y)
$\therefore$ distance between (0, y) and (-1, 0) is 2 units
$\sqrt{1+y^2}=2$
$1+y^2=4$
$y=\pm \sqrt{3}$
$\therefore$ Required circle is
$x^2+y^2\pm 2\sqrt{3}y+2=0$