A circle has its center at the midpoint of (-4, 2) and (6, 0), and its radius is 5. What is the equation of this circle?

Question

whpalmer4 · Answer

Find the midpoint of the two known points — that is your center.  You find the midpoint by averaging the x values and y values.  The average of the x values will be the x value of the midpoint, and the average of the y values will be the y value of the midpoint.

Once you have your center and radius, you can write the equation for the circle:

$$(x-h)^2 + (y-k)^2 = r^2 $$is the general formula for a circle with center at $(h,k)$.  Pay careful attention to the signs!