write the equation in standard form for the circle with center (0,5) and radius 8sqrt2
The standard form equation for a circle with center (h,k) and radius r is:
(x - h)^2 + (y - k)^2 = r^2
In this case, the center is (0,5) and the radius is 8sqrt2. Plugging those values into the equation we get:
(x - 0)^2 + (y - 5)^2 = (8sqrt2)^2
Simplifying:
x^2 + (y - 5)^2 = 128
Therefore, the equation in standard form for the circle with center (0,5) and radius 8sqrt2 is x^2 + (y - 5)^2 = 128.