# How do you write the equation for a circle with center (-4, 2) and passing through (0, 5)?

Jun 6, 2016

${x}^{2} + {y}^{2} + 8 x - 4 y - 5 = 0$

#### Explanation:

the ray is the distance between center and point

${r}^{2} = {\left(0 + 4\right)}^{2} + {\left(5 - 2\right)}^{2}$
${r}^{2} = 16 + 9$
${r}^{2} = 25$

so the requested equation is obtained by:

${\left(x + 4\right)}^{2} + {\left(y - 2\right)}^{2} = 25$
${x}^{2} + 8 x + 16 + {y}^{2} - 4 y + 4 - 25 = 0$
${x}^{2} + {y}^{2} + 8 x - 4 y - 5 = 0$