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.

C and D are unchanged, but E increases.

Step-by-step explanation:

Given equation of circle

x^2+y^2+Cx+Dy+E=0

But we know that general equation of circle is with center at (h,k)

x^2 + y^2 -2hx -2ky + (h^2 + k^2 – r^2) = 0

Comparing both equations we get,

C = -2hx

D = -2ky

As in the given question we are not changing the coordinates of center so C and D will remain unchanged.  

It also gives us

E = (h^2 + k^2 – r^2)

Decreasing r means that a lesser quantity will be subtracted from h^2 + k^2 which will increase the value of E.  

in problems involving proportions, we can use cross products to test whether two ratios are equal and form a proportion. to find the cross products of a proportion, we multiply the outer terms, called the extremes, and the middle terms, called the means.

hope it