Question

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

Answer 1

`(x+2)^2+y^2=25`

Explanation:

The standard equation of a circle is

`(x-h)^2+(y-k)^2=r^2,` where `(h, k)` is the center and `r` is the radius.

So, we're given `r=5,` meaning `r^2=25.`

Moreover, we're given `(h, k)=(-2,0)`

So, plugging the given information into the standard equation yields

`(x-(-2))^2+(y-0)^2=(5)^2`

`(x+2)^2+y^2=25`

To plot the circle, first, begin at your center, `(-2, 0).`

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, `(-2, 0),` surrounded by the points `(-2, 5), (-2,-5), (3, 0), (-7, 0)`.

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