# How do you write and equation for a circle with Center: (-4, 9) and radius: 12?

Jun 25, 2016

${x}^{2} + {y}^{2} + 8 x - 18 y - 47 = 0$

#### Explanation:

The equation of a circle with center at $\left(h , k\right)$ and radius $r$ is

${\left(x - h\right)}^{2} + {\left(y - k\right)}^{2} = {r}^{2}$ (this is equivalent to distance of a point on circumference from center being equal to radius).

Hence the equation of a circle with center at $\left(- 4 , 9\right)$ and radius $12$ is

${\left(x - \left(- 4\right)\right)}^{2} + {\left(y - 9\right)}^{2} = {12}^{2}$ or

(x+4))^2+(y-9)^2=144 or

${x}^{2} + 8 x + 16 + {y}^{2} - 18 y + 81 = 144$ or

${x}^{2} + {y}^{2} + 8 x - 18 y + 97 - 144 = 0$ or

${x}^{2} + {y}^{2} + 8 x - 18 y - 47 = 0$