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