Answer:
option: C
Step-by-step explanation:
The general form of a equation of a circle is given as:
[tex]Ax^2+By^2+Cx+Dy+E=0[/tex]
; We are given that A=B and the radius of circle is 3 units also the centre lies on y-axis.
now we consider option 3
[tex]A=1,B=1,C=0,D=-8 ,E=7.[/tex]
on putting the values of A,B,C,D and E in equation of circle we get
[tex]x^{2}+y^{2}-8y+7=0\\ \\x^2+y^2+16-16-8y+7=0\\\\x^{2}+(y-4)^2-16+7=0[/tex]
[tex]x^{2}+(y-4)^2-9=0\\ \\x^{2} +(y-4)^2=9\\\\x^{2} +(y-4)^2=3^2[/tex]
Hence, the given properties are satisfied.
Hence, option C is correct.
The value will be " a=1 b=1, C = 0, D = -8, and E = 7".
[tex]x^2+y^2-8y+7=0.[/tex]
[tex]Ax^2 + By^2+ Cx + Dy+ E= 0 \\\\r=3[/tex]
A=B
A, B, C, D, and E=?
[tex](x-a)^2 + (y-b)^2 = r^2[/tex] is another variant of the circle equation.
The center coordinates are a and b, and the radius is r.
So the equation is [tex]x^2+(y-4)^2=9[/tex].
The usual form:
[tex]So\\ A=1, B=1, C=0, D=-8,\ \ and\ \ E=7.[/tex]
OR
[tex]x^2 + y^2 - 8y + 7 = 0 \\\\x^2 + y^2 + 16 - 16 - 8y + 7 = 0\\\\ x^2 + (y - 4)^2 - 16+ 7 = 0 \\\\x^2 + (y - 4)^2 - 9 = 0\\\\ x^2 + (y - 4)^2 = 9\\\\ x^2 + (y - 4)^2 = 3^2[/tex]
Therefore, the final answer is "Option C".
Find out more information about the circle equation here:
brainly.com/question/10165274
