Answer
$\frac{(x-2)^2}{9}+\frac{(y-2)^2}{1}=1$
Work Step by Step
The standard form of the equation of the elipse when the major axis is:
- horizontal: $\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1$ in which $(h,k)$ is the center and $2a$ is the major axis length and $2b$ is the minor axis length.
- vertical: $\frac{(x-h)^2}{b^2}+\frac{(y-k)^2}{a^2}=1$ in which $(h,k)$ is the center and $2a$ is the major axis length and $2b$ is the minor axis length.
Vertices: $(0,2)~~and~~(4,2)$
The center is the midpoint: $\frac{(0,2)+(4,2)}{2}=(2,2)$
The elipse is in the horizontal position. The distance between the vertices is equal to $2a$:
$2a=4-0=4$
$a=2$
$2b=2$
$b=1$
$\frac{(x-2)^2}{3^2}+\frac{(y-2)^2}{1^2}=1$
$\frac{(x-2)^2}{9}+\frac{(y-2)^2}{1}=1$
