Answer
(a)
Center: $C(0,0)$
Vertices: $V(0,±a)=V(0,±\frac{1}{2})$
Foci: $F(0,±c)=F(0,±\frac{\sqrt 5}{6})$
(b)
Length of the major axis:
$2a=1$
Length of the minor axis:
$2b=\frac{2}{3}$
(c)
Work Step by Step
Equation of an ellipse with center at $(h,k)$ (major axis is vertical):
$\frac{(x-h)^2}{b^2}+\frac{(y-k)^2}{a^2}=1$
$9x^2+4y^2=1$
$\frac{x^2}{\frac{1}{9}}+\frac{y^2}{\frac{1}{4}}=1$
$\frac{(x-0)^2}{(\frac{1}{3})^2}+\frac{(y-0)^2}{(\frac{1}{2})^2}=1$
$h=0$
$k=0$
Center: $C(0,0)$
$a=\frac{1}{2}$
$b=\frac{1}{3}$
$c^2=a^2-b^2=\frac{1}{4}-\frac{1}{9}=\frac{5}{36}$
$c=\frac{\sqrt 5}{6}$
Vertices: $V(0,±a)=V(0,±\frac{1}{2})$
Foci: $F(0,±c)=F(0,±\frac{\sqrt 5}{6})$
Length of the major axis:
$2a=1$
Length of the minor axis:
$2b=\frac{2}{3}$
