Examples:

1) Find an equation of the circle with radius 3 and center (2, -5).
Solution:
Using the equation of a circle with r = 3, h = 2, and k = -5, we obtain
(x -2)2 + (y + 5)2 = 9

2) Sketch the graph of hte equation: x2 + y2 + 2x - 6y + 7 = 0 by first showing that it represents a circle and then finding its center and radius.
Solution:
First, group the x terms together and then the y terms together:
(x2 + 2x) + (y2 - 6y) = -7

Then we complete the square within each grouping, adding the square of half the 
coefficient of x and the square of half the coefficient of y to both sides of 
the equation: 
(x2 + 2x + 1) + (y2 - 6y + 9) = -7 + 1 + 9
(x + 1)2 + 9y - 3)2 = 3

Comparing this equation with the standard one for a circle, we see that h = -1, 
k = 3, and r = sqrt(3), so the given equation represents a circle with center at 
(-1, 3) and radius sqrt(3).  The sketch is shown below:

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