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Parameterize the intersection of the surfaces

  1. Jan 16, 2012 #1
    Parameterize the intersection of the surfaces z=x^2-y^2 and z=x^2+xy-1

    What's getting me stuck on this problem is the xy. I set x=t

    z=x^2-y^2
    z=t^2-y^2

    z=x^2+xy-1
    t^2-y^2=t^2+ty-1
    y^2=1-ty
    Thats as far as of come, I'm stuck on this
     
  2. jcsd
  3. Jan 16, 2012 #2

    Dick

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    That looks ok so far. So now you want to solve y^2=1-ty for y in terms of t, right? It's a quadratic equation. You should be able to solve that.
     
  4. Jan 16, 2012 #3
    That's the part I'm stuck on, y^2+ty-1=0; (y+?)(y-?)=0
     
  5. Jan 16, 2012 #4

    Dick

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    You don't really directly solve something like this by factoring. Do you know the quadratic formula?
     
  6. Jan 16, 2012 #5
    sorry I was thinking something else for the quadratic eqn y= -t+/- sq rt(t^2=4)/2
     
  7. Jan 16, 2012 #6

    Dick

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    That would be right, if you could clean up the formatting.
     
  8. Jan 16, 2012 #7
    then r(t)=<t, (-t+/- sq rt(t^2=4))/2, t^2-(-t+/- sq rt(t^2=4))/2> thanks for your help!
     
  9. Jan 16, 2012 #8

    Dick

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    Gack. sq rt(t^2=4)? What's that supposed to mean? And your z component is wrong. But I think you can clean this up on your own.
     
  10. Jan 16, 2012 #9
    would the Z component be z= x^2-y^2 and just put the x and y in?
     
  11. Jan 16, 2012 #10

    Dick

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    It would probably be easier to put them into z=x^2+xy-1 so you don't have to square y, don't you agree?
     
  12. Jan 16, 2012 #11
    Agreed, thanks again for all your help!
     
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