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.(adsbygoogle = window.adsbygoogle || []).push({});

(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!!!

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Equation of a parabola

**Physics Forums | Science Articles, Homework Help, Discussion**