Equations of circles

Graphing Form of a Circle
Center is at (h, k)
2 2 2
x h y k r
r is the radius of the circle

EX 1 Write an equation of a circle with
center (3, -2) and a radius of 4.
2 2 2
+x h y k r
22 2
3 + 2 4x y
2 2
3 + 2 16x y

center (-4, 0) and a diameter of 10.
2 2 2
+x h y k r
2 2 2
4 + 0 5x y
2 2
4 +y 25x

center (2, -9) and a radius of .11
222
2 9 11x y
2 2 2
+x h y k r
2 2
2 + y+9 11x

EX 4 Find the coordinates of the center and
the measure of the radius.
2 2 2
6 + 3 25x y

The center is
The radius is
The equation is
5. Find the center, radius, &
equation of the circle.
(0, 0)
12
x2 + y2 = 144

The center is
The radius is
The equation is
6. Find the center, radius, &
equation of the circle.
(1, -3)
7
(x – 1)2 + (y + 3)2 = 49

7. Graph the circle, identify
the center & radius.
(x – 3)2 + (y – 2)2 = 9
Center (3, 2)
Radius of 3

Converting from Graphing Form to
Standard
1. Move the x terms together and the
y terms together.
2. Move C to the other side.
3. Complete the square (as needed)
for x.
4. Complete the square(as needed)
for y.
5. Factor the left & simplify the right.

2 2
( 8 ) 7x x y
8. Write the standard equation of the circle.
State the center & radius.
2 2
8 7 0x y x
Center: (4, 0) radius: 3
2 2
( 4) 9x y
2 2
( 8 )16 167x x y

2 2
4 6 3x x y y
2 2
4 6 3 0x y x y
Center: (-2, 3) radius: 4
2 2
2 3 16x y
2 2
4 6 9394 4x x y y

2 2
8 2 10x x y y
2 2
2 2 16 4 20 0x y x y
2 2
4 1 7x y
2 2
8 2 1 116 1610x x y y
2 2
8 2 10 0x y x y
: (4, 1) : 7 2.6Center Radius

11. Write the general form of the equation of
the circle.
2 2
4 3 36x y
2 2
8 16 6 9 36x x y y
2 2
8 16 6 9 36 0x x y y
2 2
8 6 11 0x y x y

Equations of circles

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Equations of circles