Question 689885
T do not know what you are already supposed to know, and/or how you are expected to solve the problem, but maybe some of what follows will sound familiar.
The equation {{{x^2-y^2=9}}} represents and graphs as a hyperbola,
a set of two curves that look like an inverted set of brackets,
like a corset fastened around the origin, looking like this )+( .
For the points on those curves, {{{x^2-y^2=9}}}.
The points in between those curves have smaller {{{x^2}}} values that the points directly to their left and right on the hyperbola,
so for those points, {{{x^2-y^2<9}}}.
The points on the outside of the hyperbola have larger {{{x^2}}} values that the points at the same height (same {{{y}}}) on the hyperbola,
so for those points, {{{x^2-y^2>9}}}.
I would graph the hyperbola as dashed lines and would color the space outside the two curves, like this:
{{{graph(300,150,-10,10,-5,5,x^2-y^2>9)}}}
Maybe you are expected to make a table of (x,y) value pairs, plot the points and join them with two curves.
Maybe you know about hyperbolas, their asymptotes and vertices, and that will allow you to draw a better hyperbola.