conic sections circles

1. r2
= (x – h)2
+ (y – k)2
r is the radius must be “ – ”
(h, k) is the center
Circles
Example B. Write the equation
of the circle as shown.
The center is (–1, 3)
and the radius is 5.
Hence the equation is:
52
= (x – (–1))2
+ (y – 3)2
or
25 = (x + 1)2
+ (y – 3 )2
(–1, 3)

2. Example C. Identify the center and
the radius of 16 = (x – 3)2
+ (y + 2)2
.
Label the top, bottom, left and right
most points. Graph it.
Put 16 = (x – 3)2
+ (y + 2)2
into the
standard form:
42
= (x – 3)2
+ (y – (–2))2
Hence r = 4, center = (3, –2)
(3,–2)
Circles
r = 4

3. Example E. Use completing the square to find the center
and radius of x2
– 6x + y2
+ 12y = –36. Find the top, bottom,
left and right most points. Graph it.
We use completing the square to put the equation into the
standard form:
x2
– 6x + + y2
+ 12y + = –36 ;complete squares
x2
– 6x + 9 + y2
+ 12y + 36 = –36 + 9 + 36
( x – 3 )2
+ (y + 6)2
= 9
( x – 3 )2
+ (y + 6)2
= 32
Hence the center is (3 , –6),
and radius is 3.
Circles
(3 ,–9)
(3 , –3)
(0 ,–6) (6 ,–6)