Question

Write the equation of the circle with center at $(0,0)$ and a radius of $6$

• A. $(x-6{)}^2+y^2=36$
• B. $x^2+(y-6{)}^2=0$
• C. $x^2+y^2=36$
• D. $x^2+y^2=-36$

Answer 1

The correct option is C $x^2+y^2=36$

An equation of the circle with center $(h,k)$ and radius $r$ is

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

So, if the center is $(0,0)$ and the radius is $6$, an equation of the circle is: $(x-0{)}^2+(y-0{)}^2=6^2$

On simplifying, we get:

$x^2+y^2=36$

Hence, the equation of the circle is $x^2+y^2=36$.