Answer
(a)
Vertices: $V(±7,0)$
Foci: $F(±\sqrt {47},0)$
Eccentricity:
$e=\frac{\sqrt {47}}{7}$
(b)
Length of the major axis:
$2a=14$
Length of the minor axis:
$2b=2\sqrt 2$
(c)
Work Step by Step
$2x^2+49y^2=98$
$\frac{x^2}{49}+\frac{y^2}{2}1$
$\frac{x^2}{7^2}+\frac{y^2}{(\sqrt 2)^2}=1$
The major axis is horizontal.
Equation of an ellipse when major axis is horizontal (center at the origin):
$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$
So:
$a=7$
$b=\sqrt 2$
$c^2=a^2-b^2=49-2=47$
$c=\sqrt {47}$
(a)
Vertices: $V(±a,0)=V(±7,0)$
Foci: $F(±c,0)=F(±\sqrt {47},0)$
Eccentricity:
$e=\frac{c}{a}=\frac{\sqrt {47}}{7}$
(b)
Length of the major axis:
$2a=14$
Length of the minor axis:
$2b=2\sqrt 2$
