Answer
$${\text{circle}}$$
Work Step by Step
$$\eqalign{
& \frac{{{{\left( {x + 3} \right)}^2}}}{{16}} + \frac{{{{\left( {y - 2} \right)}^2}}}{{16}} = 1 \cr
& {\text{Multiply both sides by 16}} \cr
& {\left( {x + 3} \right)^2} + {\left( {y - 2} \right)^2} = 16 \cr
& or \cr
& {\left( {x + 3} \right)^2} + {\left( {y - 2} \right)^2} = {\left( 4 \right)^2} \cr
& {\text{The equation is written in the form }}{\left( {x - h} \right)^2} + {\left( {y - k} \right)^2} = {r^2} \cr
& {\text{Therefore,}} \cr
& {\text{The graph of the equation }}\frac{{{{\left( {x + 3} \right)}^2}}}{{16}} + \frac{{{{\left( {y - 2} \right)}^2}}}{{16}} = 1{\text{ is a circle}} \cr} $$
