# What is the center and radius of the circle with equation #x^2 + y^2 – 4x + 22y + 61 = 0#?

##### 1 Answer

Jan 3, 2016

The center is at

#### Explanation:

All the manipulations that will be done are in effort to make the equation resemble the general form of a circle:

#(x-h)^2+(y-k)^2=r^2#

Where the center is

Sort the

#x^2-4x+y^2+22y=-61#

Complete the square for the *and* right sides.

#(x^2-4x+4)+(y^2+22y+121)=-61+4+121#

#(x-2)^2+(y+11)^2=64#

Thus, the center is at