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Translate the rectangular equation to spherical

  1. Sep 9, 2012 #1
    Translate the rectangular equation to spherical and cylindrical equations.

    http://www.texify.com/img/%5CLARGE%5C%21x%5E2%2By%5E2%2B2y-3x%2Bz%5E2%3D25.gif [Broken]
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Sep 9, 2012 #2

    SammyS

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    Hello whynot314. Welcome to PF!

    What have you tried?

    Where are you stuck?

    We can't help you until you show us what you tried. It in the rules .
     
    Last edited by a moderator: May 6, 2017
  4. Sep 10, 2012 #3
    I first transformed x^2+y^2+z^2 into ρ^2

    ρ^2+2ρsinϕsinθ-3ρsinϕcosθ=25

    then factored out a ρ

    ρ(ρ+2sinϕsinθ-3sinϕcosθ)=25

    I want to solve for ρ,

    I am confused as to, weather or not subtract 25 and set it equal to zero or keep it like this and have two equations where

    ρ=25

    and


    ρ=25-2sinϕsinθ+3sinϕcosθ
     
  5. Sep 10, 2012 #4

    HallsofIvy

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    Then what you need is a good class in arithmetic! If ab= c it does NOT follow that "a= c or b= c!!

    If that isn't enough, if xy= 10, it does NOT follow that either x= 10 (and y= 1) or y= 10 (and x= 1). There are an infinite number of soutions to xy= 10.
     
  6. Sep 10, 2012 #5

    SammyS

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    How can you say ρ = 25 ?

    ρ2 + 2ρsinϕsinθ-3ρsinϕcosθ = 25 is quadratic in ρ .

    Complete the square or use the quadratic formula to solve for ρ.

    For either, you may want to rewrite your equation as:
    ρ2 + 2ρsinϕ(sinθ-cosθ) = 25​
    To complete the square, add
    [itex]\sin^2\phi\left(\sin\theta-\cos\theta\right)^2[/itex]​
    to both sides.

    To use the quadratic formula instead, subtract 25 from both sides of
    ρ2 + 2ρsinϕ(sinθ-cosθ) = 25 .​
     
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