Question

The equation x2 + y2 − 2x + 2y − 1 = 0 is the general form of the equation of a circle. What is the standard form of the equation?

Answer 1

(x − 1)2 − (y − 1)2 = 1


(x − 1)2 + (y + 1)2 = 3


(x + 1)2 + (y − 1)2 = 1


(x − 1)2 + (y + 1)2 = 1

Answer 2

Do you know how to "complete the square" ?
See https://www.khanacademy.org/math/algebra/quadratics/completing_the_square/v/completing-the-square
for how to do it.

I would complete the square on
x^2 − 2x

and complete the square on
y^2 +2y