Answer
Foci: $(0,\pm 12)$
Eccentricity$:\qquad e =\displaystyle \frac{12}{13}$
Directrices$:\displaystyle \quad y=\pm\frac{169}{12}$
Graph:
Work Step by Step
$169x^{2}+25y^{2}=4225\qquad /\div 4225$
$\displaystyle \frac{x^{2}}{25}+\frac{y^{2}}{169}=1,\qquad $
We have a vertical major axis.
$a=5,b=13$,
Foci: $(0,\pm c)$
$c=\sqrt{a^{2}-b^{2}}=\sqrt{169-25}=12$
Eccentricity$:\qquad e=\displaystyle \frac{c}{a}=\frac{12}{13}$
Directrices$:\quad y=0\displaystyle \pm\frac{a}{e}$
$y=\displaystyle \pm\frac{13}{(\frac{12}{13})}$
$y=\displaystyle \pm\frac{169}{12}$
$(y\approx 14.08)$
