How do you find the center-radius form of the equation of the circle described and graph it. center (-2,0), radius 5?

Mar 26, 2018

${\left(x + 2\right)}^{2} + {y}^{2} = 25$

Explanation:

The standard 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 and $r$ is the radius.

So, we're given $r = 5 ,$ meaning ${r}^{2} = 25.$

Moreover, we're given $\left(h , k\right) = \left(- 2 , 0\right)$

So, plugging the given information into the standard equation yields

${\left(x - \left(- 2\right)\right)}^{2} + {\left(y - 0\right)}^{2} = {\left(5\right)}^{2}$

${\left(x + 2\right)}^{2} + {y}^{2} = 25$

To plot the circle, first, begin at your center, $\left(- 2 , 0\right) .$

Then, since the radius is $5 ,$ plot a point $5$ units up, another point $5$ units down, another point $5$ units left, and a last one $5$ units right. Connect these points with arcs, resulting in a circle.

This will result in the center, $\left(- 2 , 0\right) ,$ surrounded by the points $\left(- 2 , 5\right) , \left(- 2 , - 5\right) , \left(3 , 0\right) , \left(- 7 , 0\right)$.

$$             graph{(x+2)^2+y^2=25 [-10, 10, -5, 5]}