http://www.ck12.org Chapter 9. Circles
9.7 Extension: Writing and Graphing the Equations of Circles
tions of Circles
Learning Objectives
- Graph a circle.
- Find the equation of a circle in the coordinate plane.
- Find the radius and center, given the equation of a circle and vice versa.
- Find the equation of a circle, given the center and a point on the circle.
Graphing a Circle in the Coordinate Plane
Recall that the definition of a circle is the set of all points that are the same distance from a point, called the center.
This definition can be used to find an equation of a circle in the coordinate plane.
Let’s start with the circle centered at the origin, (0, 0). If(x,y)is a point on the circle, then the distance from the
center to this point would be the radius,r.xis the horizontal distance of the coordinate andyis the vertical distance.
Drawing those in, we form a right triangle. Therefore, the equation of a circle,centered at the originisx^2 +y^2 =r^2 ,
by the Pythagorean Theorem.
Example 1:Graphx^2 +y^2 =9.
Solution:This circle is centered at the origin. It’s radius is the square root of 9, or 3. The easiest way to graph a
circle is to plot the center, and then go out 3 units in every direction and connect them to form a circle.