# Chapter 4 - Review Exercises - Page 354: 67

$\frac{(x-2)^2}{9}+\frac{(y-2)^2}{1}=1$

#### 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 $2a$: $2a=4-0=4$ $a=2$ $2b=2$ $b=1$ $\frac{(x-2)^2}{3^2}+\frac{(y-2)^2}{1^2}=1$ $\frac{(x-2)^2}{9}+\frac{(y-2)^2}{1}=1$

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