Question

The general form of the equation of a circle is Ax2 + By2 + Cx + Dy + E = 0, where A = B 0. If the circle has a radius of 3 units and the center lies on the y-axis, which set of values of A, B, C, D, and E might correspond to the circle?

Answer 1

(x-h)^2 + (y-k)^2 = r^2

r=3
(x-h)^2 + (y-k)^2 = 3^2

the center lies on the y-axis --> h=0
x^2 + (y-k)^2 = 3^2 = 9

expand
x^2 + y^2 -2ky + k^2 = 9

x^2 + y^2 -2ky + (k^2 - 9) = 0
compare to general form
A=1 , B=1 and C =0
D= -2k and E=k^2 - 9

Answer 2

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.

Step-by-step explanation:

Plato