Firstly, we'll recall the standard mathematical formula for the equation of a circle, which is:
(x - h)^2 + (y - k)^2 = r^2
where (h, k) are the coordinates for the center of the circle, and r stands for the radius of the circle. The point (h, k) means that we move h units along the x-axis and k units along the y-axis. The r, or the radius, is the distance from the center of the circle to any point on the circle.
Now let's substitute the coordinates of the given center of the circle (1, 3) and the given radius 3 into the formula.
So, h = 1, k = 3 and r = 3.
Substituting these into the formula, we get:
(x - 1)^2 + (y - 3)^2 = 3^2
Hence, the equation of the circle with the center at (1,3) and radius 3 is (x - 1)^2 + (y - 3)^2 = 3^2.
This equation gives us all the points (x, y) that lie on the circle.