# Algebra II : Graphing Circle Functions

## Example Questions

### Example Question #1 : Graphing Circle Functions

The graph of the equation

is a circle with what radius?

Explanation:

Rewrite the equation of the circle in standard form

as follows:

Since  and , we complete the squares by adding:

The standard form of the equation sets

,

so the radius of the circle is

### Example Question #2 : Graphing Circle Functions

Determine the graph of the equation

Hyperbola, centered at

Ellipse, centered at

Explanation:

The equation of a circle in standard for is:

Where the center  and the radius of the cirlce is .

Dividing by 4 on both sides of the equation yields

or

an equation whose graph is a circle, centered at (2,3) with radius = .5

### Example Question #3 : Graphing Circle Functions

Give the radius and the center of the circle for the equation below.

Explanation:

Look at the formula for the equation of a circle below.

Here  is the center and  is the radius. Notice that the subtraction in the center is part of the formula. Thus, looking at our equation it is clear that the center is  and the radius squared is . When we square root this value we get that the radius must be

### Example Question #4 : Graphing Circle Functions

Determine the equation of a circle whose center lies at the point  and has a radius of .

Explanation:

The equation for a circle with center  and radius  is :

Our circle is centered at  with radius , so the equation for this circle is :

### Example Question #5 : Graphing Circle Functions

What is the radius of the circle?

Explanation:

The parent equation of a circle is represented by . The radius of the circle is equal to . The radius of the cirle is .

### Example Question #6 : Graphing Circle Functions

What is the center of the circle expressed by the funciton ?