Answer: The correct option is (D) [tex](x-1)^2+(y-2)^2=16.[/tex]
Step-by-step explanation: We are given to select the standard form of the equation of the circle in the graph.
We know that
the standard form of the equation of a circle with center at (h, k) and radius r units is given by
[tex](x-h)^2+(y-k)^2=r^2~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
From the graph, we see that
the center of the circle at the point (1, 2).
That is, (h, k) = (1, 2).
The radius is the distance between the center and any point on the circumference of the circle. So, the radius of the circle as calculated from the graph is
r = 4 units.
Substituting the value of (h, k) and r in equation (i), we get
[tex](x-1)^2+(y-2)^2=4^2\\\\\Rightarrow (x-1)^2+(y-2)^2=16.[/tex]
Thus, the required standard equation of the circle is [tex](x-1)^2+(y-2)^2=16.[/tex]
Option (D) is correct.
