identify the vertex,focus,and directrix of the equation
y^2-4x-2y=3

This web site tells a lot about parabolas:

Parabola - Wikipedia, the free encyclopedia

(First equation)

1. axis parallel to the y-axis
2. vertex: (h,k)
3. focus: (h,k+p)
4. directrix: y=k-p

or

(Second equation)

1. axis parallel to the x-axis
2. vertex: (h,k)
3. focus: (h,k+p)
4. directrix: y=k-p

Your equation is





The x's are now on the right, the y's on the left side. Let's concentrate on the left side. That's the most difficult since we have a square term. We note that

but we need a 1 on that side also. Add a 1 to both sides.



Now factor



That looks like the second equation with k=1, p=1, h=-1.

You should be able to figure out the question now.