



 
Hi Katrina, I pasted in the graphic you sent
You have the asymptotes intersecting at (0,2) which is correct but I am not sure you have the slopes correct. To find the asymptotes, look at the equation in general form which you have
Set the right side to zero and factor the left side as a difference of squares
This is then two equations
These are the equations of the asymptotes.
Now you know the graph of the hyperbola lies in either the region of the plane shaded orange below or the region of the plane shaded green. To determine where the graph lies you just need to plot one point. The equation is
It looks like y = 2 is an easy value to substitute into the equation as it makes the first term zero, but that gives
which is impossible, so there is no point on the graph with ycoordinate equal to 2. A second easy value to substitute is x = 0 as this makes the second term zero and gives
which gives the points (0, 1) and (0, 3)
Hence the hyperbola lies in the portion of the plane shaded green. I hope this helps,  


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