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Equation of the parabola help

  1. Oct 3, 2007 #1
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
    Last edited by a moderator: May 12, 2014
  2. jcsd
  3. Oct 3, 2007 #2
    Can we find the equation of the parabola when only two points on it are known and neither of them is the focus nor the vertex?
  4. Oct 3, 2007 #3


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    No. Three points are needed. If you mean to find a specific equation, the general form for a parabola equation has three constants which must be treated as variables; the coordinate values become the known values. You will need 3 equations, and have 3 unknowns - you are looking for the three unknown constants.

    You need any three points on the curve, [tex] \[
    (x_1 ,y_1 ),\;(x_2 ,y_2 ),\;(x_3 ,y_3 )
    y_1 = ax_1^2 + bx_1 + c \\
    y_2 = ax_2^2 + bx_2 + c \\
    y_3 = ax_3^2 + bx_3 + c \\
  5. Oct 3, 2007 #4
    Well technically you could make infinitely many parabola's with two different points couldn't you?
  6. Oct 3, 2007 #5


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    I'm concerned about the way that is phrased. Do you understand that the focus of a parabola is never on the parabola?
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