# Circle equation review

Review the standard and expanded forms of circle equations, and solve problems concerning them.

## What is the standard equation of a circle?

This is the general

**standard**equation for the circle centered at $(\blueD h, \maroonD k)$ with radius $\goldD r$.Circles can also be given in

**expanded form**, which is simply the result of expanding the binomial squares in the standard form and combining like terms.For example, the equation of the circle centered at $(\blueD 1,\maroonD 2)$ with radius $\goldD 3$ is $(x-\blueD 1)^2+(y-\maroonD 2)^2=\goldD 3^2$. This is its expanded equation:

*Want to learn more about circle equations? Check out this video.*

## Practice set 1: Using the standard equation of circles

*Want to try more problems like this? Check out this exercise and this exercise.*

## Practice set 2: Writing circle equations

*Want to try more problems like this? Check out this exercise.*

## Practice set 3: Using the expanded equation of circles

To interpret the expanded equation of a circle, we should rewrite it in standard form using the method of "completing the square."

Consider, for example, the process of rewriting the expanded equation $x^2+y^2+18x+14y+105=0$ in standard form:

Now we can tell that the center of the circle is $(-9,-7)$ and the radius is $5$.

*Want to try more problems like this? Check out this exercise and this exercise.*