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How to find equation of a surface

How can I find equation of the following surface:

I have a table of data for $x,y,z$.
If I plot a graph of $y=0$,I get:

The graph has only two points of intersection. How can I find the equation of the surface given the $x,y,z$ data?

A:

Let $z=ax+by+cz+d$,
so you can rewrite the equation as
begin{align*}
a&=sqrt{x^2+y^2-zx},\
b&=sqrt{x^2+y^2+zx},\
c&=x,\
d&=y.
end{align*}
This is a Paraboloid, so it can be written as
begin{align*}
a&=sqrt{x^2+y^2}+c,\
b&=sqrt{x^2+y^2}-c.
end{align*}
Now plug in $x$, $y$ and $z$ and you can get an equation, if you want you can use functions like the implicit function theorem.
P.S. I forgot to check the initial question, sorry.

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