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