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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
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

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geerky42
 one year ago
Best ResponseYou've already chosen the best response.3Arrange 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?

geerky42
 one year ago
Best ResponseYou've already chosen the best response.3Saying 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 \(a^2 + b~a+\left(\frac{b}{2}\right)^2 \Rightarrow\left(a+\frac{b}{2} \right)^2\)
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