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Intersection of TWO QUADRICS/Conics

  1. Dec 19, 2013 #1
    1. The problem statement, all variables and given/known data

    Find all the plane (x,y) all points of intersection of two quadric:
    2x^2-xy+3y^2=36,
    3x^2-4xy+5y^2=36




    2. Relevant equations


    3. The attempt at a solution

    I want to know the general process to solve something like this. Is the problem solved by using det somehow? Or divide by y^2 and let k=x/y then make 2 equations are solve that somehow??
     
  2. jcsd
  3. Dec 19, 2013 #2
  4. Dec 19, 2013 #3
    OK, so eq 2-eq1, then use that as eq 3. Solve eq1 and eq3 as a system, which got that answer. Is this process correct?

    My class is a ring&field class. I don't see how this even related at all... No determinate needed to solve this?
     
  5. Dec 19, 2013 #4

    tiny-tim

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    hi glueball8! :smile:

    (try using the X2 button just above the Reply box :wink:)
    yes, that will give you two values for x/y, which you can then substitute into the original equations :wink:

    (and if they weren't both 36 on the RHS, of course you would multiply one of them to make the RHSs the same)
     
  6. Dec 22, 2013 #5
    Thanks, do you know what does this have to do with ring&fields (Abstract algebra)? I thought you had to use something special to solve it but apparently its just regular system of equations.
     
  7. Dec 23, 2013 #6

    tiny-tim

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    i've no idea :redface:

    anyone? :smile:
     
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