Question

The equation of the circle lying in first quadrant, which touches both the coordinates axes and the distance of it's centre from origin is $2$ units is

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

Answer 1

The correct option is D $x^2+y^2-2\sqrt{2}x-2\sqrt{2}y+2=0$


Coordinates of the centre will be,
$=(2\cos {45}^{\circ },2\sin {45}^{\circ })=(\sqrt{2},\sqrt{2})$
$\Rightarrow$Radius of the circle $=\sqrt{2}$
Required equation of the circle,
$(x-\sqrt{2}{)}^2+(y-\sqrt{2}{)}^2=(\sqrt{2}{)}^2\Rightarrow x^2-2\sqrt{2}x+2+y^2-2\sqrt{2}y+2=2\Rightarrow x^2+y^2-2\sqrt{2}x-2\sqrt{2}y+2=0$