The equation of a circle is
x2 + y2 + cx + dy + e = 0. if the radius of the circle is decreased without changing the coordinates of the center point, how are the coefficients c, d, and e affected?

First we will write different type of equation for circle so we can see how did we get coeficients C D and E

(x-x1)^2 + (y-y1)^2 = r^2 

where x,y is coordinate of a point on circle, x1,y1 are coordinates of the center of circle and r is radius of circle

after solving binomials on square we get terms like this:
-2*x*x1 and -2*y*y1

looking at like term in our given equation we can conclude that there is no "r" in those terms meaning that changing radius doesnt depend on coefficients C and D. They depend only on coordinates of the center of circle.

As for coefficient E.
if we move r^2 to left side we can see that E = x1^2 + y1^2 -r^2 meaning that if we decrease "r", E will increase.