I had read in my notes that the equation of parabola can be given by
(Equation of axis)$^2$ = (Length of Latus rectum)*(Equation of tangent at vertex)
(I don't know the systematic proof. Is there something I am missing in the equation?)
Now take look at this very basic equation of a parabola
$ y^2=4ax $
Here the equation of axis of parabola is $(y=0)$ and that of tangent at vertex is $(x=0)$
I can also write the equation of axis as $(ny=0)$ and tangent at vertex as $(mx=0)$
(where m and n are constants)
And hence using the first equation I can write the equation of parabola as
$(ny)^2 = 4a(mx)$
which gives me a completely different parabola.
I don't know where I have gone wrong. Please guide me.