Answer
$$\frac{{{x^2}}}{4} + \frac{{{y^2}}}{9} = 1$$
Work Step by Step
$$\eqalign{
& {\text{From the graph we can see that the orientation of Major Axis is}} \cr
& {\text{vertical }}\left( {{\text{along the y - axis}}} \right){\text{ and the ellipse is centered at the }} \cr
& {\text{Origin}}.{\text{ Then, the equation is of the form}} \cr
& \frac{{{x^2}}}{{{b^2}}} + \frac{{{y^2}}}{{{a^2}}} = 1 \cr
& \cr
& {\text{The length of the major axis is 6}} \cr
& {\text{2}}a = 6,\,\,\,\,a = 3 \cr
& {\text{The length of the minor axis is 4}} \cr
& 2b = 4,\,\,\,b = 2 \cr
& \cr
& \frac{{{x^2}}}{{{{\left( 2 \right)}^2}}} + \frac{{{y^2}}}{{{{\left( 3 \right)}^2}}} = 1 \cr
& \frac{{{x^2}}}{4} + \frac{{{y^2}}}{9} = 1 \cr} $$
