# What is the general form of the equation of a circle given the Center (-1,2) and Solution Point (0,0)?

Dec 11, 2015

${\left(x + 1\right)}^{2} + {\left(y - 2\right)}^{2} = 5$

#### Explanation:

The general form for a circle with center $\left(a , b\right)$ and radius $r$ is
$\textcolor{w h i t e}{\text{XXX}} {\left(x - a\right)}^{2} + {\left(y - b\right)}^{2} = {r}^{2}$

With center $\left(- 1 , 2\right)$ and given that $\left(0 , 0\right)$ is a solution (i.e. a point on the circle),
according to the Pythagorean Theorem:
$\textcolor{w h i t e}{\text{XXX}} {r}^{2} = {\left(- 1 - 0\right)}^{2} + {\left(2 - 0\right)}^{2} = 5$

and since the center is $\left(a , b\right) = \left(- 1 , 2\right)$

by applying the general formula we get:
$\textcolor{w h i t e}{\text{XXX}} {\left(x + 1\right)}^{2} + {\left(y - 2\right)}^{2} = 5$