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Homework Help: Find the Radius and Center of a Sphere, Quadric Surfaces

  1. Jul 9, 2017 #1
    1. The problem statement, all variables and given/known data

    Find the radius and center of sphere
    ρ = 28 cos ϕ.

    2. Relevant equations

    Relevant equations would be the spherical and rectangular coordinate equations.

    3. The attempt at a solution

    I started off by multiplying both sides of the equation by ρ to get

    ρ^2 = 28 ρ cosϕ

    Then this would allow me to get to the equation of a sphere which is

    x^2 + y^2 + z^2 = 28z

    I don't really know where to go from here. Could someone point me in the right direction? I can't really seem to find how to get rid of the z. I know the a^2 under x,y,z will give me the radius if I just take a.
  2. jcsd
  3. Jul 9, 2017 #2


    Staff: Mentor

    From your last equation, ##x^2 + y^2 + z^2 - 28z = 0##
    Complete the square in the z terms. You'll have a sphere whose center is at (0, 0, ?).
  4. Jul 9, 2017 #3
    You are an absolute life saver haha. Such a simple solution, I really need to learn to think outside the box... .
    Last edited: Jul 9, 2017
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