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?

To determine the effect of the radius changes to the coefficients, we need to rewrite the form of the equation into:

(x−α)²+(y−β)²=r² 
From the equation, we will see that:

C=−α∗2
D=−β∗2
and α²+β²−r²=E
where r represents the radius of the circle and α,βare the coordinate of the center of the circle.

Therefore, when the r decreases the coefficients C and D do not change but E increases.