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?

The problem ask to find the value of the of the variables in the formula where as the equation of the circle is Ax^2 + By^2 + Cx +Dy + E = 0 and the circle has a radius of 3 units and its center lies on y-axis. OS the best answer that could fit to it is that A=1, B=1,C=0, D=-8, and E=7. I hope this would help you a lot.

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calculista calculista · Answer 2 · 2018-09-28T19:00:11+02:00

the options of the question are

a) a=0 B=0 C=2 D=2 E=3

b) A=1 B=1 C=8 D=0 E=9

c) A=1 B=1, C = 0, D = -8, and E = 7

d) A = 1, B = 1, C = 8, D = 8, and E = 3

we know that

the equation of the circle in the form center-radius is equal to

[tex](x-h)^{2} +(y-k)^{2}=r^{2}[/tex]

in this problem we have

[tex](h,k)=(0,k)[/tex] ------> because the center lies on the y-axis

[tex]r=3\ units[/tex]

substitute

[tex](x-0)^{2} +(y-k)^{2}=3^{2}[/tex]

[tex](x-0)^{2} +(y-k)^{2}=3^{2}\\x^{2}+y^{2}-2yk+k^{2} -9=0[/tex]

so

[tex]A=1\\B=1\\C=0\\D=-2k\\E=(k^{2} -9)[/tex]

the answer is the option

c) a=1 b=1, C = 0, D = -8, and E = 7