The center of the given circle \((x+5)^{2} +(y+7)^{2} = 212\) is (-5, -7).
What is the general equation of a circle?
The general equation of the circle is
\((x-h)^{2} +(y-k)^{2} = r^{2}\).
Where,
(h, k) is the center of the circle.
and r is the radius of the circle.
According to the given question.
We have equation of the circle \((x+5)^{2} +(y+7)^{2} = 212\)
On comparing the above equation with the general equation of the circle
\((x-h)^{2} +(y-k)^{2} =r^{2}\)
we get h = -5 and k = -7
Therefore, the center of the given circle \((x+5)^{2} +(y+7)^{2} = 212\) is (-5, -7).
Thus, option c is correct.
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