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?

(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 1

@Luigi0210

Answer 2

@geerky42

Answer 3

Arrange equation:
\[x^2 - 2x + y^2 + 2y = 1\]

Now we need to insert something here:
\[(x^2 - 2x + \underline{\text{ ? }} )+ (y^2 + 2y + \underline{\text{ ? }}) = 1\]
So we can complete the square it. Any idea?

Answer 4

Saying we have something like \(a^2 + b~a\).

To complete the square, we should add \(\left(\frac{b}{2}\right)^2\) to both sides, so we have \(a^2 + b~a+\left(\frac{b}{2}\right)^2 \Rightarrow\left(a+\frac{b}{2} \right)^2\)

Answer 5

@mathmath333

Answer 6

@peachpi