Identify the focus, directrix, and axis of symmetry of x2=108y.

Question

anonymous · Answer

2x or x^2? @uffa678

tkhunny · Answer

Find the Vertex.  This will lead you on your way.

tkhunny · Answer

$x^{2} = 108y$

anonymous · Answer

well people do like to copy and paste alot.

anonymous · Answer

its X^2

tkhunny · Answer

That's better.  Try to remember that "inline" typing just doesn't quite carry the same meaning as what appears in your textbook.

Now, find that Vertex.

anonymous · Answer

so is the vertex (0,0)

tkhunny · Answer

Very good.  Axis of symmetry is next.  Go!

anonymous · Answer

wait how do i find that?

tkhunny · Answer

You look at it.  Vertex Form is this, in your case.  $108(y - 0) = (x-0)^{2}$.  Those 0s helped you find the Vertex.  The Axis of Symmetry is also in there.  Since the Vertex is (0,0), the Axis of Symmetry must be either x = 0 or y = 0.  Which is it.  It ALWAYS goes through the Vertex.

anonymous · Answer

so the acid of symmetry is always the vertex or no?

anonymous · Answer

axis*

tkhunny · Answer

No, the Vertex is a point.  The Axis of Symmetry is a line that contains that point.  If you fold your parabola on the Axis of Symmetry, you will see that you have exact copies on each side.