# What is the general form of the equation of a circle with a center at the origin and a radius of 9?

Dec 26, 2015

${x}^{2} + {y}^{2} = 81$

#### Explanation:

Any general circle centred at $\left(a , b\right)$ and with radius $r$ has equation ${\left(x - a\right)}^{2} + {\left(y - b\right)}^{2} = {r}^{2}$

So in this case since the centre is the origin, it implies that $a = b = 0$, and the radius $r = 9 \implies {r}^{2} = {9}^{2} = 81$.

Thus the equation reduces to ${x}^{2} + {y}^{2} = 81$.

Dec 26, 2015

${x}^{2} + {y}^{2} = {9}^{2}$

#### Explanation:

General Equation of a circle:
${\left(x - a\right)}^{2} + {\left(y - b\right)}^{2} = {r}^{2}$
where (a,b) are the coordinates of center and 'r' is the radius
since in you question center lies on origin and the radius is 9
therefore, (a,b) = (0,0) and r=9
hence, ${x}^{2} + {y}^{2} = {9}^{2}$