Question

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

Answer 1

Answer: If the center of the circle is to the right of the y-axis, C is negative and its absolute value increases as the center moves to the right. If the center is to the left of the y-axis, C is positive and its value decreases as the center moves to the right. D does not change when the center moves horizontally.

If the center of the circle is above the x-axis, D is negative and its absolute value increases as the center moves up. If the center is below the y-axis, D is positive and its value decreases as the center moves up. C does not change when the center moves vertically.

The values of C and D are not affected when the radius changes, as long as the center stays the same.

Explanation:

plato/ edmentum answer

Answer 2

Let's examine what each of this coefficients does.
Coefficient C would shift the circle along the x-axis.
Coefficient D would shift the circle along the y-axis. Both coefficients C and D would increase the radius of a circle. But since they also change the coordinates of the centre point they must stay the same.
Coefficient E changes the radius of a circle. In this case E<0, in order to keep the equation in the real domain.
The absolute value of coefficient E would get smaller as we shrink the circle.