Question

A circle which touches the axes, and whose centre is at a distance $2\sqrt{2}$ from the origin, has the equation

• A. $x^2+y^2-4x+4y+4=0$
• B. $x^2+y^2+4x-4y+4=0$
• C. $x^2+y^2+4x+4y+4=0$
• D. none of these

Answer 1

Answer: (A), (B), (C)

The correct options are
A $x^2+y^2-4x+4y+4=0$
B $x^2+y^2+4x-4y+4=0$
C $x^2+y^2+4x+4y+4=0$

Let $r$ be the radius of the circle.
The circle touches both the axes. Hence, its centre can have the coordinates $(r,r)$ or $(r,-r)$ or $(-r,r)$ or $(-r,-r)$.
The distance from the origin $=2\sqrt{2}$
Hence, $2r^2=8$
$\Rightarrow r^2=4$
$\Rightarrow r=2$
Hence,the centre can be $(2,2)$ or $(2,-2)$ or $(-2,2)$ or $(-2,-2)$. The radius of the circle is $2$
Hence, options $A,B$ and $C$ are correct.