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.
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As I am remembering, both sides could be right. If $p>0$ is any number then we can consider two parabolas: $$x^2=2py,~~(\text{or}~~x^2=-2py),~~~~y^2=2px,~~(\text{or}~~y^2=-2px) $$
Mikasa
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No I don't think you understood the question. I have posted an edited question again please answer that. – geek101 Aug 01 '14 at 17:49
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@user166748: Sorry, I am late to answer the new version. I am glad you got the proper answer finally. :-) – Mikasa Aug 02 '14 at 06:24
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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.
mathlove
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No I don't think you understood the question. I have posted an edited question again please answer that. – geek101 Aug 01 '14 at 17:48