Graph  ( x + 1)² /9 -( y - 2)²/4 =1

Solution

It is a hyperbola. There are in fact two standard forms for a hyperbola.  Following are the basics for each form.

Hence, what does all this mean?  Firstly, notice as well that one of the terms is positive and the other is negative. It will determine which direction the two parts of the hyperbola open.  If the x term is positive the hyperbola opens left & right.  Similarly, if the y term is positive the parabola opens up & down.

Both have the similar "center".  Note down that hyperbolas don't actually have a center in the sense that circles & ellipses have centers. The center is the beginning point in graphing a hyperbola.  It tells us how to obtain to the vertices and how to obtain the asymptotes set up.

The asymptotes of a hyperbola are two lines which intersect at the center & have the slopes listed above.  As you move further than out from the center the graph will get closer & closer to the asymptotes.

For the equation listed here the hyperbola will open left & right.  Its center is

 (-1, 2).  The two vertices are (-4, 2) & (2, 2). The asymptotes will have slopes ±2/3            .

Following is a sketch of this hyperbola.  Note as well that the asymptotes are indicated by the two dashed lines.