Algebra II : Graphing Circle Functions

Example Questions

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Example Question #1 : Graphing Circle Functions

Determine the graph of the equation

Ellipse, centered at

Hyperbola, 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 #2 : 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 #3 : 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 #4 : 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 #5 : Graphing Circle Functions

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

Explanation:

The equation can be rewritten so that it looks like the parent equation for a circle . After completeing the square, the equation changes from  to . From there it can be expressed as . Therefore the center of the circle is at .

Example Question #6 : Graphing Circle Functions

The graph of the equation

is a circle with what as the length of its 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 #7 : Graphing Circle Functions

What are the coordinates of the center of a circle with the equation ?

Explanation:

The equation of a circle is , in which (h, k) is the center of the circle. To derive the center of a circle from its equation, identify the constants immediately following x and y, and flip their signs. In the given equation, x is followed by -1 and y is followed by -6, so the coordinates of the center must be (1, 6).

Example Question #8 : Graphing Circle Functions

What is the radius of a circle with the equation ?

Explanation:

To convert the given equation into the format , complete the square by adding  to the x-terms and to the y-terms.

The square root of 4 is 2, so the radius of the circle is 2.

Example Question #9 : Graphing Circle Functions

What is the radius of a circle with the equation ?

Explanation:

To convert the given equation into the format , complete the square by adding  to the x-terms and to the y-terms.

The square root of 25 is 5, so the radius of the circle is 5.

Example Question #10 : Graphing Circle Functions

Which equation does this graph represent?