How do you find all points that have an x -coordinate of –4 and whose distance from point (4, 2) is 10?

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Quenchingof · Accepted Answer

We want D=10Let             (              x        1            ,              y        1            )       be             (      4      ,      2      )      Let             (              x        2            ,              y        2            )       be             (      -      4      ,              y        2            )            10    =                                        (            4            -                          (              -              4              )                        )                    2                +                              (            2            -                          y              2                        )                    2                    2      Squaring both sides we have                    (        10        =                                                            (                4                -                                  (                  -                  4                  )                                )                            2                        +                                          (                2                -                                  y                  2                                )                            2                                2                )            2            ⇒    100    =          (              8        2            )        +                  (        2        -                  y          2                )            2            ⇒    100    =    64    +          (      4      -      4              y        2            +                        (                      y            2                    )                2            )            ⇒                  (                  y          2                )            2        +    4          y      2        +    4    =    36        ⇒                  (                  y          2                )            2        +    4          y      2        -    32    =    0        ⇒          (              y        2            +      8      )              (              y        2            -      4      )        =    0  y_2 = -8; 4

How do you find all points that have an x -coordinate of –4 and whose distance from point (4, 2) is 10?

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