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Simple parabola solving problem

  1. Jul 6, 2013 #1
    Hi friends I am sticking in solving a parabola equation. Please help me in solving this issue.

    The problem is as follows -

    I have given three points which are as follows -

    [Broken]

    These points are lying on a parabola whose equation is Y2 = 4AX

    If these points are lying on this parabola hence will satisfy its equation.

    Hence

    Placing all the points in the equation Y2 = 4AX

    [Broken]

    Solving these equations I'll get -

    [Broken]

    But friends the problem is that, when I am solving these equations in different manner - - -

    [Broken]

    I am getting the wrong answer. The previous answer was right i.e. a√7 / 2.


    Why this is happening. Please friends help me in finding this issue.

    Thank you all very much in advance.
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Jul 6, 2013 #2
    The point ##(x_1, y_1) = (0, a/2)## is not compatible with the equation ##y^2 = 4Ax##.
     
  4. Jul 6, 2013 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    [itex]y^2= 4Ax[/itex] is a parabola through the origin and symmetric about x= 0. The more general form would be [itex]x= ay^2+ bx+ c[/itex] or [itex]x= a(y- y_0)^2+ x_0[/itex].

    Notice that while your form has only the single parameter, A, those have three parameters which can be determined by three equations.
     
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