```Question 334131
<pre><b>
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:

{{{x^2/a^2 - y^2/b^2}}}{{{""=""}}}{{{1}}}

or

{{{y^2/a^2 - x^2/b^2}}}{{{""=""}}}{{{1}}}

---------------------------------------------------

So both cases are below:

The two rules needed are:

1. The four corners of the fundamental rectangle of the hyperbola

{{{x^2/a^2 - y^2/b^2}}}{{{""=""}}}{{{1}}} 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

{{{y^2/a^2 - x^2/b^2}}}{{{""=""}}}{{{1}}} 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

{{{x^2/81 - y^2/36}}}{{{""=""}}}{{{1}}} 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

{{{y^2/81 - x^2/36}}}{{{""=""}}}{{{1}}} which opens upward and downward

are (6,9), (6,-9), (-6,9),(-6,-9)

Edwin</pre></b>```