Answer
Center: $(1,5)$
Foci: $(1,9)~~and~~(1,1)$
Vertices: $(1,10)~~and~~(1,5-5)=(1,0)$
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.
$\frac{(x-1)^2}{9}+\frac{(y-5)^2}{25}=1$
$\frac{(x-1)^2}{3^2}+\frac{(y-5)^2}{5^2}=1$
$a=5,~~b=3$
$c^2=a^2-b^2=25-9=16$
$c=4$
Center: $(1,5)$
The major axis is vertical:
- the foci: $(1,5+4)=(1,9)~~and~~(1,5-4)=(1,1)$
- the vertices: $(1,5+5)=(1,10)~~and~~(1,5-5)=(1,0)$
