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Equation of a parabola

  1. Nov 14, 2011 #1
    Hi! I am trying to find the equation of a parabola with vertex as (h,k) and axis parallel to the x-axis. However, I am not able to derive the correct result.
    (1) I shift the origin to the point (h,k).
    (2) Now the equation of the parabola in the new system becomes y[itex]^{2}[/itex] = 4ax.
    (3) Now, we know that when we shift the origin without rotation of axes to a point (h,k) (wrt the old system), the locus in the old system is changed by replacing x by x-h and y by y-k. This gives us the equation of the locus in the new system.
    Now, since the equation of the parabola in the new system is y[itex]^{2}[/itex]=4ax, then the equation of the parabola in the old system must be (y+k)[itex]^{2}[/itex] = 4a(x+h), as on replacing x by x-h and y by y-k in this equation, we get the equation of the parabola in the new system, which is y[itex]^{2}[/itex] = 4ax.
    Please help in finding the fault in this derivation. Thanks!!!
     
  2. jcsd
  3. Nov 14, 2011 #2

    Stephen Tashi

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    Do you want to transform a parabola whose axis is along the y-axis ( f(x) = 4a x^2 ) to one whose axis is parallel to the new x-axis? You will have to rotate the coordinate system, not simply move the origin. What form do you want the new parabola to take?
     
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