Given that the two endpoints of a diameter are (-2,-2) and (4,6), find the equation of the circle

Sure, here are the steps to find the equation of the circle:

Step 1: Find the center of the circle. The center of the circle is the midpoint of the diameter. The midpoint formula is ((x1+x2)/2, (y1+y2)/2). So, the center of the circle is ((-2+4)/2, (-2+6)/2) = (1, 2).

Step 2: Find the radius of the circle. The radius is the distance from the center of the circle to either endpoint of the diameter. The distance formula is sqrt((x2-x1)^2 + (y2-y1)^2). So, the radius of the circle is sqrt((4-1)^2 + (6-2)^2) = sqrt(9 + 16) = sqrt(25) = 5.

Step 3: Write the equation of the circle. The standard form of the equation of a circle is (x-h)^2 + (y-k)^2 = r^2, where (h, k) is the center of the circle and r is the radius. So, the equation of the circle is (x-1)^2 + (y-2)^2 = 5^2.

Therefore, the equation of the circle is (x-1)^2 + (y-2)^2 = 25.