Answer
$${\text{hyperbola}}$$
Work Step by Step
$$\eqalign{
& 9{x^2} - 16{y^2} = 144 \cr
& {\text{Divide both sides by 144}} \cr
& \frac{{9{x^2}}}{{144}} - \frac{{16{y^2}}}{{144}} = \frac{{144}}{{144}} \cr
& \frac{{{x^2}}}{{16}} - \frac{{{y^2}}}{9} = 1 \cr
& {\text{The equation is written in the form }}\frac{{{x^2}}}{{{b^2}}} - \frac{{{y^2}}}{{{a^2}}} = 1\, \cr
& {\text{Therefore,}} \cr
& {\text{The graph of the equation is a hyperbola}} \cr} $$
