The center of a circle is at (2, 3) and it has a radius of 3. What is the equation of the circle?

Feb 13, 2016

the equation of circle is ${x}^{2} + {y}^{2} - 4 x - 6 y + 4 = 0$

Explanation:

Equation of a circle with radius $r$ and center $\left(h , k\right)$ is given by

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

as center in this case is $\left(2 , 3\right)$ and $r = 3$

the equation of circle is

${\left(x - 2\right)}^{2} + {\left(y - 3\right)}^{2} = {3}^{2} = 9$ or ${x}^{2} - 4 x + 4 + {y}^{2} - 6 y + 9 = 9$

or ${x}^{2} + {y}^{2} - 4 x - 6 y + 4 = 0$