# How do you write the equation of the circle with diameter that has endpoints at (–4, –1) and (–8, –9)?

##### 1 Answer

#### Answer:

#### Explanation:

To write the equation of a circle we need to know the center and the radius. Since we know two endpoints, we know the extrema of a diameter.

The idea is the following: we will find the center as the midpoint of the diameter, and the radius as half the length of the diameter.

To find the midpoint of a segmente with extrema

In your case, this becomes

As for the length, we have the following formula:

Which in your case becomes

So, the diameter is

Now we can write the equation:

in general, given the center

Which in this case becomes