# How do you write an equation for a circle with center (-2,5) and radius of 5?

Jan 28, 2016

${x}^{2} + {y}^{2} + 4 x - 10 y + 4 = 0$

#### Explanation:

suppose,
the equation is,
${\left(x - h\right)}^{2} + {\left(y - k\right)}^{2} = {r}^{2}$
here,
$h = - 2$
$k = 5$
$r = 5$
so, the equation is,
${\left(x + 2\right)}^{2} + {\left(y - 5\right)}^{2} = {5}^{2}$
$\mathmr{and} , {x}^{2} + 4 x + 4 + {y}^{2} - 10 y + 25 = 25$
$\mathmr{and} , {x}^{2} + {y}^{2} + 4 x - 10 y + 4 = 0$