What is the center of the circle given by the equation below?
x2 + 8x + y2 - 8y + 31 = 0

A.
(4 , 4)
B.
(-4 , -4)
C.
(-4 , 4)
D.
(4 , -4)

To do this question you need to complete the square.

To do this, you need to half the coefficient of x, which in this case is 8 and put it in brackets that are squared.

This gives (x+4)^2.
Then you need minus the square of the number in the brackets, so 16.

This gives (x+4)^2-16

Then you do the same for y.

(y-4)^2-16

Then you would add these together and rearrange but it’s not necessary for your question.

The centre is the opposite of what is in the brackets.

So for x, it’s -4 and for y, it’s 4, meaning your answer is C.