# How do you graph the circle with center at (-4, 2) and radius 5 and label the center and at least four points on the circle, then write the equation of the circle?

Aug 10, 2018

See explanation...

#### Explanation:

You are probably familiar with the fact that a triangle with sides of lengths $3$, $4$ and $5$ is a right angled triangle.

That means that all of the following integer points will be on the circle of radius $5$ with centre $\left(- 4 , 2\right)$:

$\left(- 4 , 2\right) \pm \left(5 , 0\right) \text{ }$ i.e. $\left(- 9 , 2\right)$ and $\left(1 , 2\right)$

$\left(- 4 , 2\right) \pm \left(0 , 5\right) \text{ }$ i.e. $\left(- 4 , - 3\right)$ and $\left(- 4 , 7\right)$

$\left(- 4 , 2\right) \pm \left(3 , 4\right) \text{ }$ i.e. $\left(- 7 , - 2\right)$ and $\left(- 1 , 6\right)$

$\left(- 4 , 2\right) \pm \left(4 , 3\right) \text{ }$ i.e. $\left(- 8 , - 1\right)$ and $\left(0 , 5\right)$

$\left(- 4 , 2\right) \pm \left(3 , - 4\right) \text{ }$ i.e. $\left(- 7 , 2\right)$ and $\left(- 1 , - 2\right)$

$\left(- 4 , 2\right) \pm \left(4 , - 3\right) \text{ }$ i.e. $\left(- 8 , 5\right)$ and $\left(0 , - 1\right)$

The equation of a circle with centre $\left(h , k\right)$ and radius $r$ can be written:

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

So in our case, we can write:

${\left(x + 4\right)}^{2} + {\left(x - 2\right)}^{2} = 25$

graph{((x+4)^2+(y-2)^2 - 25)((x+4)^2+(y-2)^2 - 0.04) = 0 [-16.41, 6, -3.64, 7.2]}