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Math Help - equation of locus

  1. #1
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    equation of locus

    A point moves in such a way that it is always the same distance from the point F(-3, -7) as it is from the line y = -1. Determine the equation of the locus in standard form.

    This is the first time I come across a question in this form. How do I make use of the F(-3, -7) point and y = -1 line to write the equation?

    Thanks.
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  2. #2
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    Hello, shenton!

    A point moves in such a way that it is always the same distance
    from the point F(-3,-7) as it is from the line y = -1.
    Determine the equation of the locus in standard form.

    It might help you make a sketch . . .

    Let P(x,y) be any point satisfying the restriction.
    . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .________________
    The distance from F(-3,-7) to P(x,y) is: .FP .= .√(x + 3) + (y + 7)

    The distance from P(x,y) to the line y = -1 is: .y + 1
    . . . . . . . . . . .________________
    So we have: .√(x + 3) + (y + 7) .= .y + 1

    Square: .x + 6x + 9 + y + 14y + 49 .= .y + 2y + 1

    . . x + 6x + 9 .= .-12y - 48

    . . (x + 3) .= .-12(y + 4)

    This is a down-opening parabola with vertex (-3, -4).

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