Question

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?
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 increases.

Answer 1

Given,

The equation of a circle is x2 + y2 + Cx + Dy + E = 0

The radius of the circle is decreased without changing the coordinates of the center point.

As we know that, the general equation of the circle is given by,

x^2 + y^2 + 2gx +2fy +c  = 0

Comparing the given equation with the standard equation of a circle, we get,  

C = 2g and D = 2f  

as the coordinates of the center of the circle is (-g, -f) which remains unchanged

. So, we get, C and D are unchanged.

But we know that the radius of a circle is given by r = √(g^2 + f^2 - c)

Here c is E and we are given that radius is decreased which is only possible when the value of c i.e. E gets increased.

Therefore, we have, C and D are unchanged, but E increases.

Option E is correct.