http://www.ck12.org Chapter 9. Circles
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.
Example A
Graphx^2 +y^2 =9.
The center is (0, 0). Its radius is the square root of 9, or 3. Plot the center, plot the points that are 3 units to the right,
left, up, and down from the center and then connect these four points to form a circle.
Example B
Find the equation of the circle below.