Write the standard for of the equation of the circle that passes through the points at (0,8),(8,0),and (16,8). Then identify the center and radius of the circle.

I have r=8, center=(8,8). What now?

Just state the equation...

(x-8)^2 + (y-8)^2= 64

mentally sub in each of the 3 points.
All satisfy the equation.

To obtain the standard form of the equation of a circle, we need to know the center and the radius of the circle. In this case, you have correctly identified the center as (8, 8) and the radius as 8 units.

The standard form of the equation of a circle is given by:
(x - h)^2 + (y - k)^2 = r^2
where (h, k) represents the coordinates of the center of the circle, and r represents the radius.

Substituting the values we have, the equation of the circle becomes:
(x - 8)^2 + (y - 8)^2 = 8^2

Expanding the equation, we get:
(x - 8)(x - 8) + (y - 8)(y - 8) = 64

Simplifying further, the equation becomes:
x^2 - 16x + 64 + y^2 - 16y + 64 = 64

Combining like terms, we have:
x^2 + y^2 - 16x - 16y + 128 = 64

Finally, rearranging the terms, we get the standard form of the equation of the circle:
x^2 + y^2 - 16x - 16y + 64 = 0

So, the standard form equation of the circle passing through the points (0,8), (8,0), and (16,8) is x^2 + y^2 - 16x - 16y + 64 = 0. The center of the circle is (8, 8), and the radius is 8 units.