Step 1:
Find the mid-point of the vertices
Let the coordinates of the mid-point = (x , y)
Vertices = ( -2, 0 ) and (2, 0)
[tex]\begin{gathered} x\text{ = }\frac{-2\text{ + 2}}{2}\text{ = }\frac{0}{2}\text{ = 0} \\ y\text{ = }\frac{0\text{ + 0}}{2}\text{ = }\frac{0}{2}\text{ = 0} \end{gathered}[/tex]Mid - point = ( 0, 0 ) = ( h, k)
Minor axis = 4
a = 2
b = 1
Final answer
[tex]\begin{gathered} \frac{(x-h)^2}{b^2}\text{ + }\frac{(y-k)^2}{a^2}\text{ = 1} \\ \end{gathered}[/tex][tex]\frac{(x-0)^2}{1^2}\text{ + }\frac{(y-0)^2}{2^2}\text{ = 1}[/tex][tex]\frac{x^2}{1}\text{ + }\frac{y^2}{4}\text{ = 1}[/tex]