Answer: The correct option is (B). Its image is attached below.
Step-by-step explanation: We are given to select the graph that represents the circle with equation as follows:
[tex]x^2+y^2=9~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We know that the standard equation of a circle with center at the point (h, k) and radius r units is given by
[tex](x-h)^2+(y-k)^2=r^2.[/tex]
From equation (i), we have
[tex]x^2+y^2=9\\\\\Rightarrow(x-0)^2+(y-0)^2=3^2.[/tex]
Comparing the above equation with the standard equation of a circle, we get
Center, (h, k) = (0, 0) and radius, r = 3 units.
We draw the graph of the circle with center at the origin (0, 0) and radius 3 units in the attached figure below.
We see that the graph of the circle is same as the one provided in option (B).
Thus, option (B) is CORRECT.
