Question

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

A) C, D, and E are unchanged.

B) C increases, but D and E are unchanged.

C) C and D decrease, but E is unchanged.

D) C, D, and E increase.

E) C and D are unchanged, but E decreases.

Answer 1

Hello,

Answer D:

The circle having (a,b) as center and R as radius has for equation:

(x-a)²+(y-b)²=R²
==>x²+y²-2ax-2by+a²+b²-R²=0

If R decreases then a²+b²-R² increases.

C and D are unchanged and E increases

Answer 2

x and y are the center point so since C and D are multiplied by x an y they would remain the same

E = the center points squared plus the radius squared.

Since the radius is getting smaller E would also decrease

Answer is E