Question

Write an equation for a circle with a diameter that has endpoints at (–4, –1) and (–8, –9).

Answer 1

You need the center of the circle. That will be the midpoint of the diameter. Do you know how to find the midpoint of 2 points?

Then you need the radius. First use the distance formula to find the length of the diameter. Then take half of that for your radius.

Then put the center (h,k) and the radius r into the form for a circle:

\[(x-h)^2+(y-k)^2=r^2\]

Answer 2

Remember, all a circle is, is a collection of points that are all equidistant (r) from a fixed point (h,k) in the plane. So the circle equation is very closely related to the distance equation (really, it just IS the distance equation, with both sides squared.)

:)