http://www.ck12.org Chapter 9. Conics
Example B
Turn the following equation into graphing form for a circle. Identify the center and the radius.
36 x^2 + 36 y^2 − 24 x+ 36 y− 275 = 0
Solution: Complete the square and then divide by the coefficient ofx^2 andy^2
36 x^2 − 24 x+ 36 y^2 + 36 y= 275
36(
x^2 −^23 x+)
+ 36 (y^2 +y+ ) = 27536(
x^2 −^23 x+^19)
+ 36
(
y^2 +y+^14)
= 275 + 4 + 9
36
(
x−^13) 2
+ 36
(
y+^12) 2
= 288
(
x−^13) 2
+
(
y+^12) 2
= 8
The center is(^13 ,−^12 ). The radius is
√
8 = 2
√
2.
Example C
Write the equation of the following circle.