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Math Help - Locus

  1. #1
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    Locus

    Determine the equation of the locus of a point which moves so that its distance from P(5,2) is two-thirds its distance from the x-axis.

    Please help me solve this problem and show the solution... Thanks!
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  2. #2
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    Quote Originally Posted by lance View Post
    Determine the equation of the locus of a point which moves so that its distance from P(5,2) is two-thirds its distance from the x-axis.

    Please help me solve this problem and show the solution... Thanks!
    Hint: a parabola is the locus of points that are equidistant from a point (the focus) and a line (the directrix). I'd advise you to research how to find the equation of a parabola using the focus and directrix.
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    Quote Originally Posted by lance View Post
    Determine the equation of the locus of a point which moves so that its distance from P(5,2) is two-thirds its distance from the x-axis.

    Please help me solve this problem and show the solution... Thanks!
    Treat this as a word problem:

    Distance from P(5,2) =
    \sqrt( (x-5)^2+(y-2)^2)

    Distance from x-axis =
    |y|

    So the locus is:
    \sqrt( (x-5)^2+(y-2)^2) = \frac{2}{3}|y|
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