Graphs of Circles
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Equations of Circles

Circle with Center at
 Origin (0,0)


where the center is (0,0)
 and the radius is r.


center (0,0)
radius = 5

 

Circle with Center at
 Point (h,k)


where the center is (h,k)
 and the radius is r



center (4,4)
radius = 5

Did you notice that the formula for the circle with the center at the origin
is just a special case of the formula for a circle at point (h,k)?
When h = 0 and k = 0 (for the origin), the formula becomes

Where does the circle formula
come from?

Using the distance formula, the radius of the circle at the right is represented by


Equation of a Circle

 

 

Example 1:  Write the equation of a circle with center at (3,-5) and a radius of 3.

Answer:

 Notice how the coordinate of -5 appears
as (y + 5)2

 

Example 2:  Given the equation of a circle, , what are the coordinates of the center and the radius?

Answer:


The center is (-3,6)
and the radius is
 

 Notice how the answer for the radius is left in radical form.  You should not estimate an answer into decimal form unless told to do so, or unless working in a real world measurement situation.  It is hard to measure a radical number of feet.