New Zealand
Level 8 - NCEA Level 3

# Introduction to Circles

Lesson

When we looks at graphs of functions or relations, we concentrate our focus on key characteristics of a graph.

For example, when we look at a parabola of a quadratic function, we might focus on the turning point or the $x$x intercepts.

If we examine the graph of a hyperbola, we'll concentrate our focus on the intersection of the vertical and horizontal asymptote.

Now we're interested in examining the graph of a circle, and to do that we need to concentrate our focus on two key characteristics.

## Characteristics of a Circle Graph

If you were to guess what a key feature of a circle might be, what would you say?

Probably the radius. This is certainly a key feature which we'll need to focus on for these graphs.

The other feature, which you might not guess, is the coordinate of the centre of the circle.

On the graph below, you can see, by inspection, that the centre of the circle is $(2,-5)$(2,5)

We can determine the radius of the circle by counting the number of units from the centre, out to the left or right of the centre, or directly up or down from the centre. So for this graph the radius is $4$4 units.

#### Worked Examples

##### QUESTION 1

Consider the following.

1. Plot four points such that they are all exactly $4$4 units away from the origin.

2. Considering the four points plotted in the previous part, what shape is formed by connecting the points with four straight paths?

triangle

A

B

circle

C

triangle

A

B

circle

C
3. As the number of points we plot and connect increases towards infinity, what shape do we approach?

octagon

A

circle

B

decagon

C

octagon

A

circle

B

decagon

C

##### QUESTION 2

Consider the circle in the graph.

1. State the coordinates of the centre in the form $\left(a,b\right)$(a,b).

2. State the diameter.

### Outcomes

#### M8-1

Apply the geometry of conic sections

#### 91573

Apply the geometry of conic sections in solving problems