ANSWER
[tex]\frac{ {x}^{2} }{ 16} + \frac{ {y}^{2} }{ 9} = 1[/tex]
EXPLANATION
The given ellipse has a vertex at (4,0), a co-vertex at (0,3), and a center at the origin.
The equation of an ellipse with vertices on the x-axis and center at the origin is:
[tex] \frac{ {x}^{2} }{ {a}^{2} } + \frac{ {y}^{2} }{ {b}^{2} } = 1[/tex]
The ellipse has vertex at (4,0) , hence a=4.
Also the co-vertex is at (0,3) , b=3
We substitute the values into the equation to get:
[tex] \frac{ {x}^{2} }{ {4}^{2} } + \frac{ {y}^{2} }{ {3}^{2} } = 1[/tex]
[tex] \frac{ {x}^{2} }{ 16} + \frac{ {y}^{2} }{ 9} = 1[/tex]
