http://www.ck12.org Chapter 9. Circles
9.12 Circles in the Coordinate Plane
Here you’ll learn how to find the standard equation for circles given their radius and center. You’ll also graph circles
in the coordinate plane.
What if you were given the length of the radius of a circle and the coordinates of its center? How could you write
the equation of the circle in the coordinate plane? After completing this Concept, you’ll be able to write the standard
equation of a circle.
Watch This
MEDIA
Click image to the left for more content.CK-12 Foundation: Chapter9CirclesintheCoordinatePlaneA
MEDIA
Click image to the left for more content.James Sousa:Write the Standard Formof a Circle
Guidance
Recall that a circle is the set of all points in a plane that are the same distance from 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 (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 andyis the vertical distance. This forms a right triangle.
From the Pythagorean Theorem, the equation of a circlecentered at the originisx^2 +y^2 =r^2.
The center does not always have to be on (0, 0). If it is not, then we label the center(h,k). We would then use the
Distance Formula to find the length of the radius.
r=√
(x−h)^2 +(y−k)^2If you square both sides of this equation, then you would have the standard equation of a circle. The standard
equation of a circle with center(h,k)and radiusrisr^2 = (x−h)^2 +(y−k)^2.