Question

The equation of the circle touching both negative axes and having radius 3 is given by

• A. $x^2+y^2-6x-6y+9=0$
• B. $x^2+y^2+6x-6y+9=0$
• C. $x^2+y^2+6x+6y+9=0$
• D. $x^2+y^2+6x+6y+4=0$

Answer 1

The correct option is C $x^2+y^2+6x+6y+9=0$

Since the circle touches both negative axes and the radius is $3$

Center will be $(-3,-3)$

The equation of the circle with centre $(h,k)$ and the radius $a$ is,

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

Equation of the circle having centre $(-3,-3)$ and radius $3$ is given by
$(x+3{)}^2+(y+3{)}^2=(3{)}^2$
$\Rightarrow y^2+x^2+6x+6y+9=0$.