Answer
(a)
Center: $C(0.0)$
Vertices: $V(±4,0)$
Foci: $F(±2\sqrt {3},0)$
(b)
Length of the major axis:
$2a=8$
Length of the minor axis:
$2b=4$
(c)
Work Step by Step
Equation of an ellipse with center at $(h,k)$ (major axis is horizontal):
$\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1$
$x^2+4y^2=16$
$\frac{x^2}{16}+\frac{y^2}{4}=1$
$\frac{(x-0)^2}{4^2}+\frac{(y-0)^2}{2^2}=1$
$h=0$
$k=0$
Center: $C(0.0)$
$a=4$
$b=2$
$a^2=b^2+c^2$
$c^2=a^2-b^2=4^2-2^2=16-4=12$
$c=2\sqrt {3}$
Vertices: $V(±a,0)=V(±4,0)$
Foci: $F(±c,0)=F(±2\sqrt {3},0)$
Length of the major axis:
$2a=8$
Length of the minor axis:
$2b=4$
