Answer
Foci:$\quad (\pm 3,0)$
Eccentricity$:\qquad e =\displaystyle \frac{3}{4}$
Directrices$:\displaystyle \quad x=\pm\frac{16}{3}$
Graph:
Work Step by Step
$7x^{2}+16y^{2}=112\qquad/\div 112$
$\displaystyle \frac{x^{2}}{16}+\frac{y^{2}}{7}=1,\qquad a=4,b=\sqrt{7}$
We have a horizontal major axis.
Foci:$\quad (\pm c,0)$
$c=\sqrt{a^{2}-b^{2}}=\sqrt{16-7}=3$
Eccentricity$:\qquad e=\displaystyle \frac{c}{a}=\frac{3}{4}$
Directrices$:\displaystyle \quad x=0\pm\frac{a}{e}$
$x=\displaystyle \pm\frac{4}{(\frac{3}{4})}$
$x=\displaystyle \pm\frac{16}{3}$
