# Find equation of circle whose radius is 3 and center is origin??

Feb 22, 2018

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

#### Explanation:

The general equation of a circle is:

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

We want a circle with an a center $\left(h , k\right)$ centered at the origin.
Therefore $\left(h , k\right) = \left(0 , 0\right)$

We also want a radius $3$ so ${r}^{2} = {\left(3\right)}^{2} = 9$

Given these values, we can substitute into our equation to get:

${\left(x - 0\right)}^{2} + {\left(y - 0\right)}^{2} = 9$

Simplify and we get the equation:

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

This is the equation we want and its graph looks like

graph{x^2+y^2=9 [-10, 10, -5, 5]}