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Math Help - Finding equation of curve form a point using equal distance

  1. #1
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    Finding equation of curve form a point using equal distance

    Hi guys, need help with this problem please,

    A point P(x, y) moves in the x-y plane such that the distance from the line x=3 is always equal to the distance form the point (-6, 2).

    Prove that the locus of P can be represented by a curve C with equation
    (y+2)^2 = 9(2x-3).
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  2. #2
    MHF Contributor alexmahone's Avatar
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    Re: Finding equation of curve form a point using equal distance

    Quote Originally Posted by Blizzardy View Post
    Hi guys, need help with this problem please,

    A point P(x, y) moves in the x-y plane such that the distance from the line x=3 is always equal to the distance form the point (-6, 2).

    Prove that the locus of P can be represented by a curve C with equation
    (y+2)^2 = 9(2x-3).
    The distance between P(x, y) and the line x = 3 is x - 3.
    The distance between P(x, y) and (-6, 2) is \sqrt{(x+6)^2+(y-2)^2.

    Equate the two and simplify to find the locus of P.
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