Answer
Eccentricity: $e=\frac{c}{a}=\frac{\sqrt {29}}{6}$
Vertices: $(±6,0)$
Work Step by Step
$7x^2+36y^2=252$
$\frac{x^2}{36}+\frac{y^2}{7}=1$
$\frac{x^2}{6^2}+\frac{y^2}{(\sqrt 7)^2}=1$
The major axis is horizontal.
Standard form when major axis is horizontal:
$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$
So: $a=6$ and $b=\sqrt 7$
$a^2=b^2+c^2$
$c^2=a^2-b^2=36-7=29$
$c=\sqrt {29}$
$e=\frac{c}{a}=\frac{\sqrt {29}}{6}$
Vertices when major axis is horizontal:
$(±a,0)=(±6,0)$
