Completing The Square Of Circles Classwork (Page 2 of 4) in pdf

Completing The Square Of Circles Classwork Page 2

Learning Goal: How Do You Use Completing the Square to Write the Equation of a

Circle in Center-Radius Form?

Now, if we "multiply out" the example

we will get:

When multiplied out, we obtain the

"general form"

of the equation of a circle.

Notice that in this form we can clearly see that the

equation of a circle has both x

and y

terms and

these terms have the same coefficient (usually 1).

When the equation of a circle appears in "general form", it is often beneficial to convert the

equation to "center-radius" form to easily read the center coordinates and the radius for

graphing.

Example: Convert

into center-radius form.

This conversion requires use of the technique of

completing the square.

We will be creating two perfect square trinomials within the equation.

• Start by grouping the x related terms together

and the y related terms together. Move any

numerical constants (plain numbers) to the other

side.

• Get ready to insert the needed values for

creating the perfect square trinomials.

Remember to balance both sides of the equation.

• Find each missing value by taking half of the

"middle term" and squaring. This value will

always be positive as a result of the squaring

process.

• Rewrite in factored form.

You can now read that the center of the circle is at (2, 3) and the radius is

Completing The Square Of Circles Classwork Page 2