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.