Answer
Foci:$\quad(\pm 3,0)$
Eccentricity$:\qquad e =\displaystyle \frac{3}{5}$
Directrices$:\displaystyle \quad x=\pm\frac{25}{3}$
Graph:
Work Step by Step
Write in standard form.
$16x^{2}+25y^{2}=400\qquad/\div 400$
$\displaystyle \frac{x^{2}}{25}+\frac{y^{2}}{16}=1,\qquad$
Major axis is horizontal with $a=5,b=4$,
Foci:$\quad(\pm 3,0)$
Foci:$\quad(\pm c,0)$
$c=\sqrt{a^{2}-b^{2}}=\sqrt{25-16}=3$
Eccentricity$:\qquad e=\displaystyle \frac{c}{a}=\frac{3}{5}$
Directrices$:\displaystyle \quad x=0\pm\frac{a}{e}$
$x=\displaystyle \pm\frac{5}{\frac {3}{5}}$
$x=\displaystyle \pm\frac{25}{3}$
