Answer
Foci:$\quad(\pm 1,0)$
Eccentricity$:\qquad e =\displaystyle \frac{1}{\sqrt{10}}$
Directrices$:\quad x=\pm 10$
Graph:
Work Step by Step
$9x^{2}+10y^{2}=90\qquad /\div 90$
$\displaystyle \frac{x^{2}}{10}+\frac{y^{2}}{9}=1,\qquad $
We have a vertical major axis.
$a=\sqrt{10},b=3$,
Foci:$\quad(\pm c,0)$
$c=\sqrt{a^{2}-b^{2}}=\sqrt{10-9}=1$
Eccentricity$:\qquad e=\displaystyle \frac{c}{a}=\frac{1}{\sqrt{10}}$
Directrices$:\displaystyle \quad x=0\pm\frac{a}{e}$
$x=\displaystyle \pm\frac{\sqrt{10}}{\frac{1}{\sqrt{10}}}$
$x=\pm 10$
