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Math Help - Hyperbola problem

  1. #1
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    Unhappy Hyperbola problem

    Find the equation of the path that moves so that its distance from (4,0) is twice its distance from the line x = 1
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by ^_^Engineer_Adam^_^ View Post
    Find the equation of the path that moves so that its distance from (4,0) is twice its distance from the line x = 1
    Take a point (u,v) on the path. Its distance from the line x=1 is |u-1|, and its
    distance from (4,0) is sqrt[(u-4)^2+v^2], so:

    sqrt[(u-4)^2+v^2] = 2|u-1|

    now we square:

    (u-4)^2+v^2 = 4(u-1)^2

    which simplifies to:

    3 u^2 - v^2 = 12.

    Now replace u by x and v by y to get the equation with standard veriables:


    3 x^2 - y^2 = 12.

    RonL
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