Given a circle with the center (13,16) any point on the circle (14,14) identify the equation of the circle

The standard equation for a circle is:

(x - h)^2 + (y - k)^2 = r^2. (h, k) is your center point, which is (13, 16).

You have h and k so all you need to find for is r. For this, you would use the distance formula and find the distance between your point on the circle and your center point. This distance would be the radius.

By now you would have gotten all your necessary information, so you would end up with (x - 13)^2 + (y - 16)^2 = (radius)^2.