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Homework Help: Prove 3 distinct points lying on the some curve

  1. Sep 22, 2010 #1
    1. The problem statement, all variables and given/known data

    Given points (p1, q1), (p2, q2), (p3, q3) in the plane with p1, p2, p3 distinct, show that they lie on some curve with equation y = a + bx + cx2.

    It should be related to matrix but I have no idea about this question. Could anyone help? Thanks!

    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Sep 23, 2010 #2

    hunt_mat

    User Avatar
    Homework Helper

    One way to examine this question is given these three point you could find out, what a,b, and c is satisfied for this equation. So you know that:
    [tex]
    \begin{array}{ccc}
    q_{1} & = & ap_{1}+bp_{1}+cp_{1} \\
    q_{2} & = & ap_{2}+bp_{2}+cp_{2} \\
    q_{3} & = & ap_{3}+bp_{3}+cp_{3}
    \end{array}
    [/tex]
    This is a system of linear equations with unknowns a,b and c, the system can be solved via matrix methods.
     
  4. Sep 23, 2010 #3
    Thanks for your help!
    But I don't understand how the equation y = a + bx +cx2 can be transformed into the form y = ax + bx + cx
     
  5. Sep 23, 2010 #4

    hunt_mat

    User Avatar
    Homework Helper

    Because it can't. I made a typo, sorry! The equations should read:
    [tex]
    \begin{array}{ccc}
    q_{1} & = & ap_{1}+bp_{1}+cp_{1}^{2} \\
    q_{2} & = & ap_{2}+bp_{2}+cp_{2}^{2} \\
    q_{3} & = & ap_{3}+bp_{3}+cp_{3}^{2}
    \end{array}
    [/tex]

    Mat
     
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