The equation x² + y² − 2x + 6y + 3 = 0 is equivalent to (x − 1)² + (y + 3)² = 7
Equation of a circle
The standard equation of a circle is expressed as
x² + y² + 2gx + 2fy + C = 0
Given the equation x² + y² − 2x + 6y + 3 = 0. Using the completing the square method to write its equivalent
x² - 2y + y² + 6y + 3 = 0
( x² - 2y + 1) - 1 +(y² + 6y + 9) - 9+ 3 = 0
(x-1)² - 1 +(y + 3)² - 6 = 0
(x-1)² + (y + 3)² = 7
Hence the equation x² + y² − 2x + 6y + 3 = 0 is equivalent to (x − 1)² + (y + 3)² = 7
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