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Some review problems

  1. Jan 24, 2012 #1
    1. The problem statement, all variables and given/known data

    I'm having some trouble remembering how to do this in a refresher course...

    sketch the intersection of (x^2)+(y^2)+(z^2)=3 and z<0
    sketch the intersection of z=2(x^2)+2(y^2) and z=4-(x^2)-(y^2)


    2. Relevant equations



    3. The attempt at a solution

    I think the first one is a circle with points at 1 and -1 on each axis, not too sure if there's a certain method I'm supposed to use to figure this out with though.
     
  2. jcsd
  3. Jan 24, 2012 #2

    lanedance

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    Homework Helper

    note quite... the first is the half the surface of a sphere below zero

    one way that may help is too look at the intesection with a plane (x=0,y=0,z=0) are good

    then you either need to recognise the form or think about how one viarable relates toteh other the other

    eg. for 2)
    z=2(x^2)+2(y^2)

    x=0
    z=2(y^2)

    x=0
    z=2(x^2)

    these are both idenitical parabolas

    z=c>0
    c/2=(x^2)+(y^2)

    cuts in the cy planes give circles, so this a circular paraboloid,

    you should try drawing each of the parbaolas and a circle in 3D perspective on paper
     
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