The equation \(x^2 + y^2 - 2x + 2y - 1 = 0\) is the general form of the equation of a circle. What is the standard form of the equation?

x^2 + y^2 - 2x + 2y - 1 = 0
(x^2 - 2x) + (y^2 + 2y) - 1 = 0
(x^2 - 2x + 1) + (y^2 + 2y + 1) - 1 - 1 - 1 = 0
(x - 1)^2 + (y + 1)^2 - 3 = 0
(x - 1)^2 + (y + 1)^2 = 3

Answered by vivindalka | 2024-06-10

( x − 1 ) 2 + ( y + 1 ) 2 = 3 ;

Answered by lisboa | 2024-06-12

The equation x 2 + y 2 − 2 x + 2 y − 1 = 0 can be rewritten in standard form as ( x − 1 ) 2 + ( y + 1 ) 2 = 3 . This indicates the center of the circle is at ( 1 , − 1 ) with a radius of 3 ​ .
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Answered by lisboa | 2024-11-04