Answer: The correct option is
(B) \((x-4)^2+(y+5)^2=30.25.\)
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
\((x-h)^2+(y-k)^2=r^2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~``(i)\)
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
\((x-4)^2+(y-(-5))^2=(5.5)^2\\\\\Rightarrow (x-4)^2+(y+5)^2=30.25.\)
Thus, the required equation of the given circle is \((x-4)^2+(y+5)^2=30.25.\)
Option (B) is CORRECT.
