# How do you write the equation for a circle with center at (-1,3) passes through the point (-1,4)?

Apr 22, 2016

${\left(x + 1\right)}^{2} + {\left(y - 3\right)}^{2} = 1$

#### Explanation:

$O = \left(- 1 , 3\right)$
$P = \left(- 1 , 4\right)$

r=sqrt((-1+1)^2+(4-3)^2

$r = \sqrt{0 + 1}$

$r = 1 \text{ radius of circle}$

$\text{general equation for circle which it has a center of (a,b) and a radius of r}$
${\left(x - a\right)}^{2} + {\left(y - b\right)}^{2} = {r}^{2}$

$r = 1 \text{ "a=-1" } b = 3$

${\left(x + 1\right)}^{2} + {\left(y - 3\right)}^{2} = 1$