# How do you find the center and radius of the circle given x^2+(y+2)^2=4?

Nov 24, 2016

#### Explanation:

The standard form for the equation of a circle is:

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

where $\left(x , y\right)$ is any point on the circle, $\left(h , k\right)$ is the center, and r is the radius.

I suggest that you modify any given equation into this form and then report the easily observed values.

Change the + 2 to - -2:

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

Insert a -0 in the x term:

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

Write the constant as a square:

${\left(x - 0\right)}^{2} + {\left(y - - 2\right)}^{2} = {2}^{2}$

It is easily observed that the center is $\left(0 , - 2\right)$ and the radius is 2.