dodsonSancliz
Answered

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?

Verified Answer :

meerkat18

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.

calculista

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

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

in this problem we have

\((h,k)=(0,k)\) ------> because the center lies on the y-axis

\(r=3\ units\)

substitute

\((x-0)^{2} +(y-k)^{2}=3^{2}\)

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

so

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

the answer is the option

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


Related Questions