# How do you graph (x+4)^2+(y-1)^2=9?

Jul 7, 2018

A circle with a radius of $3$, and its center located at $\left(- 4 , 1\right)$.

#### Explanation:

Given: ${\left(x + 4\right)}^{2} + {\left(y - 1\right)}^{2} = 9$.

Notice that the equation for a circle is given by:

${\left(x - a\right)}^{2} + {\left(y - b\right)}^{2} = {r}^{2}$

where:

• $\left(a , b\right)$ are the coordinates of the circle's center

• $r$ is the radius of the circle

Here, we get $\left(a , b\right) = \left(- 4 , 1\right)$, and $9 = {3}^{2}$.

So, this equation shows us a circle with a radius of $3$ and has a center located at $\left(- 4 , 1\right)$.

Here is a graph of the circle:

graph{(x+4)^2+(y-1)^2=9 [-10, 10, -5, 5]}

Jul 7, 2018

See below:

#### Explanation:

The good thing is that this equation is in standard form

${\left(x - h\right)}^{2} + {\left(y - k\right)}^{2} = {r}^{2}$

With center $\left(h , k\right)$ and radius $r$. In our example, we have

${\left(x + 4\right)}^{2} + {\left(y - 1\right)}^{2} = 9$

This tells us that we have a center at $\left(- 4 , 1\right)$, and a radius of $3$.

To think about graphing the radius, a radius of $3$ is just the distance from the center of the circle to any endpoint.

After we interpret this information, we get the following graph:

graph{(x+4)^2+(y-1)^2=9 [-10, 10, -5, 5]}

Hope this helps!