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:

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

`y^2/25-x^2/4=1`

We have:

`y^2/25=1`

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 a north-south opening hyperbola, so the slopes of the asymptotes will be given by

`+-a/b`

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:

510-5-10510-5-10xyOpen image in a new page

Asymptotes and `y`-intercepts (& vertices in this case).

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

510-5-10510-5-10xyOpen image in a new page

"North-South" hyperbola (in green) with its asymptotes (in magenta color).

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