Answer: The correct option is
(B) [tex](x-4)^2+(y+5)^2=30.25.[/tex]
Step-by-step explanation: We are given to select the correct standard form of the equation of the circle shown in the figure.
The standard equation of a circle with center at the point (h, k) and radius of length r units is given by
[tex](x-h)^2+(y-k)^2=r^2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~``(i)[/tex]
For the given circle, as noted from the figure, we have
center, (h, k) = (4, -5) and radius, r = 5.5 units.
Therefore, from equation (i), we get
[tex](x-4)^2+(y-(-5))^2=(5.5)^2\\\\\Rightarrow (x-4)^2+(y+5)^2=30.25.[/tex]
Thus, the required equation of the given circle is [tex](x-4)^2+(y+5)^2=30.25.[/tex]
Option (B) is CORRECT.
