How to find the center, radius, x- and y- intercepts and graph of the circle : x 2 + y 2 − 2 x − 4 y − 4 = 0?

Question

How to find the center, radius, x- and y- intercepts and graph of the circle :       x    2    +      y    2    −  2  x  −  4  y  −  4  =  0?

Helen House · Accepted Answer

Step 1. Standardize the equation by converting it.The equation&#039;s standard form is                     (        x        -        h        )            2        +                  (        y        -        k        )            2        =          r      2      .We make the conversion by &quot;&quot;completing the square&quot;&quot;.            x      2        +          y      2        -    2    x    -    4    y    -    4    =    0              x      2        +          y      2        -    2    x    -    4    y    =    4              (              x        2            -      2      x      )        +          (              y        2            -      4      y      )        =    4              (              x        2            -      2      x      +      1      )        -    1    +          (              y        2            -      4      y      +      4      )        -    4    =    4              (              x        2            -      2      x      +      1      )        -    1    +          (              y        2            -      4      y      +      4      )        -    4    =    4                      (        x        -        1        )            2        -    1    +                  (        y        -        2        )            2        -    4    =    4                      (        x        -        1        )            2        +                  (        y        -        2        )            2        =    9  Step 2. Locate the centre.The centre is at (      h    ,    k  ) = (      x    ,    y  ) = (      1    ,    2  ).Step 3. Calculate the radius.The radius is       r    =          9        =    3  .Step 4. Calculate the       y  -intercepts.                    (        x        -        1        )            2        +                  (        y        -        2        )            2        =    9  Set       x    =    0  .                    (        0        -        1        )            2        +                  (        y        -        2        )            2        =    9        1    +                  (        y        -        2        )            2        =    9                      (        y        -        2        )            2        =    9    -    1    =    8        y    -    2    =    ±          8        =    ±    2          2            y    =    2    ±    2          2      The       y  -intercepts are at (      0    ,    2    -          2      ) and (      0    ,    2    +          2      ).Step 4. Calculate the       x  -intercepts.                    (        x        -        1        )            2        +                  (        y        -        2        )            2        =    9  Set       y    =    0  .                    (        x        -        1        )            2        +                  (        0        -        2        )            2        =    9                      (        x        -        1        )            2        +    4    =    9                      (        x        -        1        )            2        =    9    -    4                      (        x        -        1        )            2        =    5        x    -    1    =    ±          5            x    =    1    ±          5      The x-intercepts are at (      1    -          5        ,    0  ) and (      1    +          5        ,    0  ).

How to find the center, radius, x- and y- intercepts and graph of the circle : x^2+y^2-2x-4y-4=0?

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