The general form for the equation of a circle in the coordinate plane is given as:
GENERAL Form
Equation
of a circle
Converting to
Standard Form
We can rewrite general form equations to standard form equations using
a process called completing the square. Converting to standard form is
useful when determining the center and radius of the circle.
Use the steps below to convert the given equation to standard form.
Then identify the radius and center of the circle.
Steps
Given: x + y - 2x+6y-6= 0
O Group the x-terms together and the
y-terms together. Move the constant
to the right side of the equation.
Take half of the linear X-term and
square it. Add this value to both sides
of the equation.
Take half of the linear y-term and
square it. Add this value to both sides
of the equation.
You have created two perfect square
trinomials. Rewrite them in factored
form as squared binomials.
Identify the center and radius of the
circle.
Gina Wilson (Al Things Algebra®, LLC), 2015-2019