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

[math]\frac{\left(x-3\right)^2}{16}-\frac{\left(y+1\right)^2}{25}=1[/math][br][br]Horizontal or Vertical? [br]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. [br][br]Center: The center would be (3,-1)[br][br]Vertices: note that since it is horizontal, we will use the value of a=4 to find the vertices.[br]they will be (7,-1) and (-1,-1).[br][br]Foci: Use [math]c^2=a^2+b^2[/math] and [math]c=\sqrt{41}[/math][br]So the foci are [math]\left(3+\sqrt{41},-1\right)[/math] and [math]\left(3-\sqrt{41},-1\right)[/math][br]note that this is approximately [math]\left(9.4,-1\right)[/math] and [math]\left(-3.4,-1\right)[/math][br][br]If you use the tools above and move them appropriately, you will see this is true.