Answer
(a)
Center: $C(0,0)$
Vertices: $V(0,±6)$
Foci: $F(0,±4\sqrt 2)$
(b)
Length of the major axis:
$2a=12$
Length of the minor axis:
$2b=4$
Work Step by Step
Equation of an ellipse with center at $(h,k)$ (major axis is vertical):
$\frac{(x-h)^2}{b^2}+\frac{(y-k)^2}{a^2}=1$
$\frac{x^2}{4}+\frac{y^2}{36}=1$
$\frac{(x-0)^2}{2^2}+\frac{(y-0)^2}{6^2}=1$
$h=0$
$k=0$
Center: $C(0,0)$
$a=6$
$b=2$
$a^2=b^2+c^2$
$c^2=a^2-b^2=6^2-2^2=36-4=32$
$c=4\sqrt 2$
Vertices: $V(0,±a)=V(0,±6)$
Foci: $F(0,±c)=F(0,±4\sqrt 2)$
Length of the major axis:
$2a=12$
Length of the minor axis:
$2b=4$
