There was a typo of x for y, in one of the two places, so
I had to do both cases, since I couldn't tell whether it
was meant to be:


or


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So both cases are below:
The two rules needed are:
1. The four corners of the fundamental rectangle of the hyperbola


which opens right and left are
are (a,b), (a,-b), (-a,b),(-a,-b)
2. The four corners of the fundamental rectangle of the hyperbola


which opens upward and downward
are (b,a), (b,-a), (-b,a),(-b,-a)
Therefore,
1. The four corners of the fundamental rectangle of the hyperbola


which opens right and left are
are (9,6), (9,-6), (-9,6),(-9,-6)
2. The four corners of the fundamental rectangle of the hyperbola


which opens upward and downward
are (6,9), (6,-9), (-6,9),(-6,-9)
Edwin