How to find the center and radius of the circle x 2 + y 2 + 4 x - 8 y + 4 = 0 ?

Question

How to find the center and radius of the circle             x      2        +          y      2        +    4    x    -    8    y    +    4    =    0  ?

loise9oa · Accepted Answer

The                     general form of the equation of a circle             is                              ∣                                                                                                                                a                      a                                                                                                                                  x                      2                                        +                                          y                      2                                        +                    2                    g                    x                    +                    2                    f                    y                    +                    c                    =                    0                                                                                                              a                      a                                                                                        ∣                                            ̲                                ¯                    with centre =                               ∣                                                                                                                                a                      a                                                                                                                                  (                                                                                                    -                            g                                                                                -                            f                                                                                              )                                                                                                                                  a                      a                                                                                        ∣                                            ̲                                ¯                    and radius =                               ∣                                                                                                                                a                      a                                                                                                                                                                                                                g                            2                                                    +                                                                                                      f                            2                                                    -                                                c                                                                                                                                                        a                      a                                                                                        ∣                                            ̲                                ¯                                x      2        +          y      2        +    4    x    -    8    y    +    4    =    0                 is in this form      We must first determine g, f, and c in order to determine the center and radius.By comparing the coefficients of  &#039;like terms&#039; in the given equation with the general form.2g = 4 → g = 2 , 2f = -8 → f = -4 and c = 4      ⇒                 centre        =          (      -      g      ,      -      f      )        =          (      -      2      ,      4      )      and radius       =                            2          2                +                              (            -            4            )                    2                -        4              =                  4        +        16        -        4              =    4  Alternatively Use the method of                     completing the square            Add                     (                  1          2                          coefficient of x/y terms                )            2                     to both sides                  (              x        2            +      4      x                        +4                    )        +          (              y        2            -      8      y                        +16                    )        =                  4+16              -    4        ⇒                  (        x        +        2        )            2        +                  (        y        -        4        )            2        =    16  The                     standard form of the equation of a circle             is                              ∣                                                                                                                                a                      a                                                                                                                                                          (                        x                        -                        a                        )                                            2                                        +                                                                  (                        y                        -                        b                        )                                            2                                        =                                          r                      2                                                                                                                                  a                      a                                                                                        ∣                                            ̲                                ¯                    where (a ,b) are the coordinates of the centre and r, the radius.By comparison of equation with standard form.a = -2 , b = 4 and r = 4Thus centre = (-2 ,4) and radius = 4

How to find the center and radius of the circle x^2+y^2+4x-8y+4=0?

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