Circles Intro

1. Block 1
Circles Introduction

2. x 0 3 4 5 -3 -4 -5
y
x2
+ y2
= 25

3. x 0 3 4 5 -3 -4 -5
y ±5 ±4 ±3 0 ±4 ±3 0
x2
+ y2
= 25
(0 , 5)
(0 , -5)
(3 , 4)
(3 , -4)
etc.

4. Uses of Circles
Wheels
Cogs
Time
Coins
Roads
Jewellery
3D – Balls

5. Drawing a Circle
Need to know
Where to draw it.
How big to make it.
→ Centre
→ Radius

6. Circles
Introduction

7. What is to be learned?
• How to find the equation of a circle with
centre the origin

8. Straight Line
Need
• Gradient
• Point

9. Circle
Need
• Centre
• Radius

10. Centre The Origin
radius = 5
(5,0)
(0,5)
(-5,0)
(0,-5)
5
3
4
(3,4)
x
yr
x2
+ y2
= r2

11. Making Equation
Centre Origin Radius 7
x2
+ y2
= 49
Centre Origin Radius 12
x2
+ y2
= 144

12. Given Equation
x2
+ y2
= 64
Centre Origin Radius 8
x2
+ y2
= 80
Centre Origin Radius √80
2x2
+ 2y2
= 32
x2
+ y2
= 16
Centre Origin Radius 4

13. Circle – Centre Origin
Equation is in form:
x2
+ y2
= r2
Ex1. x2
+ y2
= 36
Centre (0,0) and radius 6
Ex2. Centre (0,0) and radius 11
x2
+ y2
= 121

14. Ex 3. Circle x2
+ y2
= 90
Centre (0,0) Radius √90
Point (6 , 7) inside, outside or on circle?
Using Dist Formula
d2
= (6 – 0)2
+ (7 – 0)2
= 85
d = √85
Inside
√√9090
√√8585
(6 , 7)(6 , 7)
(0 , 0)