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Homework Help: Finding the equation of a surface?

  1. Sep 15, 2012 #1
    1. The problem statement, all variables and given/known data

    2 Questions.

    1)Find an equation for the surface consisting of all points P for which the distance from P to the x-axis is 5 times the distance from P to the yz-plane.

    2)Find an equation for the surface consisting of all points that are equidistant from the point (−3, 0, 0) and the plane x = 3.

    2. Relevant equations

    3. The attempt at a solution

    1)The only thing I can think of is an ellipsoid with an equation similar to 5x^2+y^2+z^2=1

    Is that correct? Or am I totally off?

    2) I feel a parabolic cylinder would work here (opening facing toward point) but not sure how to find the equation.
  2. jcsd
  3. Sep 15, 2012 #2


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    Science Advisor
    Homework Helper
    Gold Member

    In both cases take a variable point ##(x,y,z)##, calculate the various distances, and use the given relations. You will undoubtedly have to square things to simplify the equations.
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