# What is the general form of the equation of a circle with its center at (-2, 1) and passing through (-4, 1)?

Mar 22, 2016

${\left(x + 2\right)}^{2} + {\left(y - 1\right)}^{2} = 4$

#### Explanation:

$\text{first ; let's find the radius of circle:}$
$\text{Center: } \left(- 2 , 1\right)$
$\text{Point: } \left(- 4 , 1\right)$
$\Delta x \text{=Point(x)-Center(x)}$
$\Delta x = - 4 + 2 = - 2$
$\Delta y \text{=Point(y)-Center(y)}$
$\Delta y = 1 - 1 = 0$
$r = \sqrt{\Delta {x}^{2} + \Delta {y}^{2}}$
$r = \sqrt{{\left(- 2\right)}^{2} + 0}$
$r = 2 \text{ radius}$

$\text{now ; we can write the equation}$
$C \left(a , b\right) \text{ center's coordinates}$
${\left(x - a\right)}^{2} + {\left(y - b\right)}^{2} = {r}^{2}$

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

${\left(x + 2\right)}^{2} + {\left(y - 1\right)}^{2} = 4$