Answer
(a)
Center: $C(0,0)$
Vertices: $V(0,±5)$
Foci: $F(0,±4)$
(b)
Length of the major axis:
$2a=10$
Length of the minor axis:
$2b=6$
(c)
Work Step by Step
Equation of an ellipse with center at $(h,k)$ (major axis is vertical):
$\frac{(x-h)^2}{b^2}+\frac{(y-k)^2}{a^2}=1$
$\frac{x^2}{9}+\frac{y^2}{25}=1$
$\frac{(x-0)^2}{3^2}+\frac{(y-0)^2}{5^2}=1$
$h=0$
$k=0$
Center: $C(0,0)$
$a=5$
$b=3$
$a^2=b^2+c^2$
$c^2=a^2-b^2=5^2-3^2=25-9=16$
$c=4$
Vertices: $V(0,±a)=V(0,±5)$
Foci: $F(0,±c)=F(0,±4)$
Length of the major axis:
$2a=10$
Length of the minor axis:
$2b=6$
