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