How to find the center and radius of the circle given x 2 + y 2 + 8 x - 6 y = 0 ?

Question

How to find the center and radius of the circle given             x      2        +          y      2        +    8    x    -    6    y    =    0  ?

Izabelle Riddle · Accepted Answer

We need                    (        a        +        b        )            2        =          a      2        +    2    a    b    +          b      2                          (        a        -        b        )            2        =          a      2        -    2    a    b    +          b      2      Complete the x and y squares.            x      2        +          y      2        +    8    x    -    6    y    =    0              x      2        +    8    x    +          y      2        -    6    y    =    0              x      2        +    8    x    +                                        (                          8              2                        )                    2                      +          y      2        -    6    y    +                                        (                          6              2                        )                    2                      =                                        (                          8              2                        )                    2                      +                                        (                          6              2                        )                    2                                x      2        +    8    x    +                                        (            4            )                    2                      +          y      2        -    6    y    +                                        (            3            )                    2                      =                                        (            4            )                    2                      +                                        (            3            )                    2                                        (        x        +        4        )            2        +                  (        y        -        3        )            2        =    25    =          5      2      This is the equation of a circle, center             (      -      4      ,      3      )       and radius       =    5  graph{(x^2+y^2+8x-6y)=0 [-15.25, 13.23, -3.42, 10.82]}

How to find the center and radius of the circle given x^2+y^2+8x-6y=0?

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