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Surface with specifications

  1. Sep 29, 2011 #1
    1. The problem statement, all variables and given/known data
    Find an equation for the surface consisting of all points p for which the distance from P to the x-axis is twice the distance from P to the yz-plane. Identify the surface.
    2. Relevant equations



    3. The attempt at a solution

    [tex]2\sqrt{(x_p-x)^2+(y_p-0)^2+(z_p-0)^2}=\sqrt{(x_p-0)^2+(y_p-y)^2+(z_p-z)^2}[/tex]

    I square both sides simplify and move over to one side yielding:

    [tex]3(x_p^2)+(3y_p^2+2y_py-y^2)+(3z_p^2+2zz_p-z^2)=0[/tex]


    from here my natural intuition says to complete the square or factor but you can't do either. Where did I go wrong?
     
  2. jcsd
  3. Sep 29, 2011 #2

    LCKurtz

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    Way too complicated. You don't need any p subscripts. The nearest point to (x,y,z) on the x axis is (x,0,0) and the nearest in the yz plane is (0,y,z). Use those.
     
  4. Sep 29, 2011 #3
    Thanks.

    You wind up with the cone [tex]4y^2+4z^2=x^2[/tex]
     
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