# 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

${x}^{2} + {y}^{2} = {9}^{2}$
${\left(x - a\right)}^{2} + {\left(y - b\right)}^{2} = {r}^{2}$
hence, ${x}^{2} + {y}^{2} = {9}^{2}$