The standard equation for a circle is
(x-h)^2 + (y-k)^2 = r^2
where the center is at point (h,k) and r is the radius.
To investigate this, check first if the quadratic equations are a perfect square. This is determined by dividing the middle term by 2 and taking its square. If it equals to the third term, it is a perfect square.
For (x^2 - 10x +25): (-10/2)^2 = 25 (perfect square)
For (y^2 - 16y + 64): (-16/2)^2 = 64 (perfect square)
Then, we simplify the equation by factoring:
(x - 5)^2 + (y -- 8)^2 = 16
Thus, the center is at point (5,8)
Also, the radius is square root of 16, which is 4.
