Answer
$$\frac{{{x^2}}}{{16}} + \frac{{{y^2}}}{9} = 1$$
Work Step by Step
$$\eqalign{
& {\text{Lenght of the major axis }}2a \cr
& 2a = 8 \cr
& a = 4 \cr
& \cr
& {\text{Lenght of the minor axis }}2b \cr
& 2b = 6 \cr
& b = 3 \cr
& \cr
& {\text{The equation of the ellipse is given by: }}\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1 \cr
& \frac{{{x^2}}}{{{{\left( 4 \right)}^2}}} + \frac{{{y^2}}}{{{{\left( 3 \right)}^2}}} = 1 \cr
& \frac{{{x^2}}}{{16}} + \frac{{{y^2}}}{9} = 1 \cr
& \cr
& {\text{Graph}} \cr} $$
