Question

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

• A. $x^2+y^2+4x+4y=0$
• B. $x^2+y^2+4x+4y+2=0$
• C. $x^2+y^2-2x-2\sqrt{2}y+\sqrt{2}=0$
• D. $x^2+y^2+4x+4y+4=0$

Answer 1

The correct option is D $x^2+y^2+4x+4y+4=0$

Centre of circle touching both axis is at $(a,a),$
Given that distance of centre from $(0,0)$ is $2\sqrt{2}$
$\therefore \left|\sqrt{2}a\right|=2\sqrt{2}$
$a=2$ or $a=-2$
$\therefore$ equation of circle is
$(x-a{)}^2+(y-a{)}^2=a^2$
$x^2+y^2-4x-4y+4=0$
$\therefore or(x+a{)}^2+(y+a{)}^2=a^2$
$x^2+y^2+4x+4y+4=0$