First, we recognise that it is a north-south opening hyperbola, with a = 5 and b = 2 . It will look similar to Example 1 above, which was also a north-south opening hyperbola.

We need to find:

• The y-intercepts (there are no x-intercepts for this example)
• The asymptotes

y-intercepts: Simply let x = 0 in the equation given in the question:

We have:

Solving gives us 2 values (as expected):

y = -5 and y = 5

Alternatively, we note that the vertices of the hyperbola are a units from the centre of the hyperbola. In this example, it means our vertices will be at x = 0 and y = -5 and y = 5.

Aymptotes: We have an east-west opening hyperbola, so the slopes of the asymptotes will be given by

In this example, a = 5 and b = 2. So the slopes of the asymptotes will be simply:

-5/2 and 5/2.

The equations for the asymptotes, since they pass through (0, 0), are given by:

y = -5x/2 and y = 5x/2

So we are ready to include the above information on our graph:

All that remains is to complete the arms of the hyperbola, making sure that they get closer and closer to the asymptotes, as follows: