Answer
$F(\pm\sqrt{3},0)$
Eccentricity$:\qquad e =\displaystyle \frac{\sqrt{3}}{3}$
Directrices$:\quad x=\pm 3\sqrt{3}$
Graph:
Work Step by Step
Write in standard form.
$6x^{2}+9y^{2}=54\qquad /\div 54$
$=\displaystyle \frac{x^{2}}{9}+\frac{y^{2}}{6}=1,\qquad a=6,b=\sqrt{6}$
The major axis is horizontal.
$c=\sqrt{a^{2}-b^{2}}=\sqrt{9-6}=\sqrt{3}$
$F(\pm\sqrt{3},0)$
Eccentricity$:\qquad e=\displaystyle \frac{c}{a}=\frac{\sqrt{3}}{3}$
Directrices$:\displaystyle \quad x=0\pm\frac{a}{e}$
$x=\displaystyle \pm\frac{3}{\frac{\sqrt{3}}{3}}$
$x=\pm 3\sqrt{3}$
