How to graph x 2 + y 2 + x - 6 y + 9 = 0 ?

Question

How to graph             x      2        +          y      2        +    x    -    6    y    +    9    =    0  ?

Natalia Arroyo · Accepted Answer

Complete the square for both       x   and       y              x      2        +          y      2        +    x    -    6    y    +    9    =    0              x      2        +    x    +          y      2        -    6    y    =    -    9                      (        x        +                  1          2                )            2        -                  (                  1          2                )            2        +                  (        y        -        3        )            2        -                  (        -        3        )            2        =    -    9                      (        x        +                  1          2                )            2        -                  (                  1          2                )            2        +                  (        y        -        3        )            2        -                  (        -        3        )            2        =    -    9                      (        x        +                  1          2                )            2        +                  (        y        -        3        )            2        =          1      4                          (        x        +                  1          2                )            2        +                  (        y        -        3        )            2        =                  (                  1          2                )            2      As a result, we can see that it is a circle             1      2       and centre             (      -              1        2            ,      3      )      graph{x^2 + y^2 + x - 6y + 9 = 0 [-6, 6, -1, 5]}

How to graph x^2+y^2+x-6y+9=0?

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