Answer
$\frac{(x-5)^2}{25}+\frac{(y-6)^2}{36}=1$
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: $(5,0)~~and~~(5,12)$
The center is the midpoint: $\frac{(5,0)+(5,12)}{2}=(5,6)$
The elipse is in the vertical position. The distance between the vertices is equal to $2a$:
$2a=12-0=12$
$a=6$
$2b=10$
$b=5$
$\frac{(x-5)^2}{5^2}+\frac{(y-6)^2}{6^2}=1$
$\frac{(x-5)^2}{25}+\frac{(y-6)^2}{36}=1$
