Writing an equation of a circle in standard form

Example:  Write the equation of a circle in standard form.

Start by grouping the x terms together, grouping the y terms together and moving the constant to the other side of the equation.

Use completing the square on the group of x terms and the group of y terms.

To find the number that completes the square for the x group, start with the coefficient of the x term, half it and square it.  The coefficient of the x term is 4

To find the number that completes the square for the y group, start with the coefficient of the y term, half it and square it.  The coefficient of the y term is -8

Add these numbers to the group of x terms and the group of y terms.  Be careful to maintain the balance of the equation by adding the numbers to both sides of the equation.

Now the group of x terms is a perfect square trinomial and will factor to be a binomial squared.  The group of y terms will do the same.

The equation of the circle is written in standard form where it is easy to recognize the center and radius of the circle.

The center is (-2,4) and the radius is 9.