The equation of a circle is x^2 + y^2 + Cx + Dy + E = 0. If the radius of a circle is decreased without changing the coordinates of the center point, how are the coefficients C, D, and E effected

Let's examine what each of this coefficients does. 
Coefficient C would shift the circle along the x-axis. 
Coefficient D would shift the circle along the y-axis. Both coefficients C and D would increase the radius of a circle. But since they also change the coordinates of the centre point they must stay the same.
Coefficient E changes the radius of a circle. In this case E<0, in order to keep the equation in the real domain. 
The absolute value of coefficient E would get smaller as we shrink the circle.