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

Answer:

#(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]}