Below you'll find the tool to see how every horizontal hyperbola works.
Please take a few minutes and study how changing certain values affects the equation

Example Problem: Identify all key features of the Hyperbola

Horizontal or Vertical?
This Hyperbola is horizontal. The positive portion of the formula uses x. It no longer matters which has the greater value of a or b.
Center: The center would be (3,-1)
Vertices: note that since it is horizontal, we will use the value of a=4 to find the vertices.
they will be (7,-1) and (-1,-1).
Foci: Use and
So the foci are and
note that this is approximately and
If you use the tools above and move them appropriately, you will see this is true.