Answer: The correct option is (A) (-5, 8).
Step-by-step explanation: We are given to find the center of the circle represented by the following equation :
\((x+5)^2+(y-8)^2=1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\)
We know that
the STANDARD equation of a circle with center at the point (h, k) and radius of length r units is given by
\((x-h)^2+(y-k)^2=r^2.\)
From equation (i), we have
\((x+5)^2+(y-8)^2=1\\\\\Rightarrow (x-(-5))^2+(y-8)^2=1^2.\)
Comparing the above equation with the standard form, we get
center, (h, k) = (-5, 8).
Thus, the required center of the given circle is (-5, 8).
Option (A) is CORRECT.
