This document provides examples of finding the center and radius of circles from their equations. It shows that if a circle equation is given as x^2 + y^2 + 2gx + 2fy + c = 0, then the center is (-g, -f) and the radius is the square root of g^2 + f^2 - c. It works through multiple examples, equating coefficients to find g, f, and c, and then uses this formula to determine the center and radius.

1. Block 1
More Circle Stuff

2. What is to be learned?
• How to get the centre and radius from the
equation

3. (x – 3)2
+ (y + 4)2
= 36
centre (3 , -4) radius 6
x2
+ 4x + y2
– 6y = 20
x2
+ y2
+ 4x – 6y – 20 = 0
(x + 2)2
– 4 + (y – 3)2
– 9= 20
(x + 2)2
+ (y – 3)2
= 33
centre (-2, 3) radius √33
x2
+ y2
+ 4x – 6y – 20 = 0
÷(-2)
√(-2)2
+ 32
+ 20

rearrange
complete
square(x + 2)2
+ (y – 3)2
= 20 + 4 + 9

4. x2
+ y2
+ 4x – 6y – 20 = 0
x2
+ y2
+ 2gx + 2fy + c = 0
equating coefficients

5. x2
+ y2
+ 4x – 6y – 20 = 0
x2
+ y2
+ 2gx + 2fy + c = 0
equating coefficients

6. x2
+ y2
+ 4x – 6y – 20 = 0
x2
+ y2
+ 2gx + 2fy + c = 0
equating coefficients
2g = 4

7. x2
+ y2
+ 4x – 6y – 20 = 0
x2
+ y2
+ 2gx + 2fy + c = 0
equating coefficients
2g = 4 2f = -6 c = -20
g = 2, f = -3
centre (-2, 3)
centre (-g , -f) radius = √(g2
+ f2
– c)
= √(22
+ (-3)2
+ 20)
= √33

8. x2
+ y2
+ 8x – 4y + 16 = 0
x2
+ y2
+ 2gx + 2fy + c = 0
equating coefficients
2g = 8 2f = -4 c = 16
g = 4, f = -2
centre (-4, 2)
centre (-g , -f) radius = √(g2
+ f2
– c)
= √(42
+ (-2)2
– 16)
= √4
= 2

9. Getting Radius and Centre
If given equation of circle it is vital to find
centre and
radius
If no brackets use
x2
+ y2
+ 2gx + 2fy + c = 0
centre (-g , -f) radius = √(g2
+ f2
– c)

10. x2
+ y2
+ 8x – 4y – 10 = 0
x2
+ y2
+ 2gx + 2fy + c = 0
equating coefficients
2g = 8 2f = -4 c = -10
g = 4, f = -2
centre (-4, 2)
centre (-g , -f) radius = √(g2
+ f2
– c)
= √(42
+ (-2)2
+ 10)
= √30

11. x2
+ y2
– 10x + 2y = 14
x2
+ y2
+ 2gx + 2fy + c = 0
equating coefficients
2g = -10 2f = 2 c = -14
g = -5, f = 1
centre (5, -1)
centre (-g , -f) radius = √(g2
+ f2
– c)
= √((-5)2
+ 12
+ 14)
= √40
Key Question Find centre and radius
x2
+ y2
– 10x + 2y – 14 = 0