Example 2

Note that the only difference between this example and the previous one is that the 9 and 25 have traded places. How does this change the shape of the hyperbola? Is there a change in the orientation from horizontal to vertical? The answer is no. Recall that orientation of a hyperbola is not determined by the sizes of the denominators in the terms of the standard equation of the hyperbola. Rather, orientation is determined by which variable (x or y) is in the ``positive'' term. Hence, as is the case in the previous example, this hyperbola is also horizontally oriented. The switch between the 9 and 25 simply changes the shape of the branches. The openings of the branches appear to be wider(????). See FIGURE H5.

Note that difference in shape (between this example and the previous) can also be seen in the equations of the asymptotes. Now we see that

and

Thus, the slope of the asymptotes is now , not as in the previous example. As the branches of the hyperbolas are drawn and ``squeeze'' close to the asymptotes, they will have more room to grow, if you will, than they had in the previous example. This shows us the true effect of switching the places of the 9 and 25 in these two examples.