## anonymous one year ago 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

1. foreverandalways13

@Luigi0210

2. anonymous

@geerky42

3. geerky42

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?

4. geerky42

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 $$a^2 + b~a+\left(\frac{b}{2}\right)^2 \Rightarrow\left(a+\frac{b}{2} \right)^2$$

5. anonymous

@mathmath333

6. anonymous

@peachpi