Question

what is the equation of parabola

Answer 1

The following are some examples of equations of parabolas in x-y plane.

the vertex is at origin and a gives the distance focus from vertex.
[tex] x^{2} = 4 a y \\ y^{2} = 4 a x \\ [/tex]

passes through origin vertex at A/2B 
$y = A x - B x^{2}$

another one
               [tex] x = A y - B y^{2} \\ [/tex]

vertex at (x1,y1) and focal length =  a

           $(x-x1)^{2} = 4 a (y-y1)$

well, the following
         $Ax^{2} + Bxy + C y^{2} + Wx + U y + V = 0$
represents  parabola  if B² = 4 AC and more conditions ....
        

Answer 2

y^2=4ax  and  x^2=4ay is the equation of parabola