# How do you find the equation of a circle with Center (-2, 1), radius = 4?

Jun 7, 2018

${\left(x + 2\right)}^{2} + {\left(y - 1\right)}^{2} = 16$

#### Explanation:

The equation of a circle is based mainly off the Pythagorean Theorem, ${a}^{2} + {b}^{2} = {c}^{2}$.

In the case of a circle, the equation restricts the potential $x$ and $y$ values of points that satisfy the equation to ones which have the same $c$ value, or are the same distance from the center.

The general form of the equation of a circle is

${\left(x - h\right)}^{2} + {\left(y - k\right)}^{2} = {r}^{2}$

Where $\left(h , k\right)$ is the center of the circle, and
$r$ is the radius of the circle.

If you look closely, you can see that any point that is $r$ units away from the center of the circle would satisfy the equation, through the same property utilized in the Pythagorean Theorem.

If you plug in the point given and the radius given, you get

${\left(x - \left(- 2\right)\right)}^{2} + {\left(y - 1\right)}^{2} = {4}^{2}$ or
${\left(x + 2\right)}^{2} + {\left(y - 1\right)}^{2} = 16$