Hello, Troy.

Equation for a circle:

r^2 = (x - h)^2 + (y - k)^2, where the center is (h, k) and the radius is r.

You are given the ENDPOINTS of the diameter. Therefore, you should immediately think to use the MIDPOINT formula. That is, (h, k) = [(10 + 4)/2, (4 + 10)/2] = (7,7)

And now, use the equation above:

r^2 = (10 - 7)^2 + (4 - 7)^2 = 9 + 9 = 18

And therefore, we now have the equation:

(x - 7)^2 + (y - 7)^2 = 18Standard form circle's equation that you are looking for

With this information, you should be able to answer all the questions regarding the circle (center of graph .. (h,k)), radius, etc, etc).