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

1 Answer
Mar 26, 2018

(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]}