# Equation of a Circle

Every circle can be written as an equation in the form:

$(x-h)^2+(y-k)^2=r^2$

in which the coordinate $(h,k)$ is the center of the circle and $r$ is the radius of the circle. Any point $(x,y)$ that makes the equation true is on the circle.

When you are given the equation of a circle, you can pull a lot of information from that equation, and even draw the circle based on the information that you pull out.

Example:

$(x-3)^2+(y-2)^2=16$

Looking at this equation, you know that the center of the circle is $(3,2)$.

Graph that point:

Then, pull the radius. $r^2=16$, so $r=4$. To graph the circle, plot 4 points that are 4 units from the center (these will help you draw your circle).

Finally, connect those 4 points to draw the circle:

You can also write the equation of a circle by pulling the center, any point on the circle, and/or, the radius.

#### Practice Problems:

## Equation of a Circle

Using the following equations, find the center and radius of the circle:

- $(x-5)^2+(y-9)^2=81$
- $(x-2)^2+(y-4)^2=25$
- $(x+4)^2+(y-7)^2=49$
- $(x+6)^2+(y+1)^2=16$

Graph the following circles:

- $(x+3)^2+(y+2)^2=4$
- $(x-1)^2+(y-1)^2=9$
- $(x+2)^2+(y+1)^2=16$

Test to see if the following points are on the circle with equation $(x-4)^2+(y-5)^2=81$:

- $(13,14)$
- $(4,-4)$
- $(2,2)$
- $(0,5)$

Write the equations for the following circles:

#### Answer Key: