Question

Equation of circles which touch both the axes and whose centres are at a distance of $2\sqrt{2}$ units from origin are

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

Answer 1

The correct option is A $x^2+y^2\pm 4x\pm 4y+4=0$

Since $h=k$ (radius )

$\sqrt{h^2+k^2}=2\sqrt{2}$

$h^2+k^2=8$

$2h^2=8$ (Taking circle $1^{st}$ Quad)

$h=2$

$\therefore k=2$ in

$\therefore$ center $=(2,2)$

Eqn. of circle having centre

$(h,k)$ & radius $=r$

$(x-h{)}^2+(y-k{)}^2=r^2$

$\therefore (x-2{)}^2+(y-2{)}^2=4$