Equation of parabola confusion

Question

I am having a confusion regarding the equation of a parabola. My teacher told me that it is in the form (axis of parabola)^2=4(vertex tangent). I feel that (vertex tangent)^2 should be 4(axis of parabola). Please help.

Answer 1

As I am remembering, both sides could be right. If $p>0$ is any number then we can consider two parabolas: $$x^2=2py,~~(\text{or}~~x^2=-2py),~~~~y^2=2px,~~(\text{or}~~y^2=-2px) $$

Answer 2

Are the followings what you want?

1) $y^2=4px\ (p\not =0)$. The vertex is the origin. The axis of symmetry is the $x$-axis. The focus is $F(p,0)$ and the directrix is $x=-p$.

2) $x^2=4py\ (p\not =0)$. The vertex is the origin. The axis of symmetry is the $y$-axis. The focus is $F(0,p)$ and the directrix is $y=-p$.

In general, $(y-n)^2=4p(x-m)\ (p\not =0)$. The vertex is $(m,n)$. The axis of symmetry is $y=n$. The focus is $F(p+m,n)$ and the directrix is $x=m-p$...and so on.