Answer
Foci:
$(0, -\sqrt{2})$ and $(0, \sqrt{2})$.
Work Step by Step
Write the equation in standard form:
$7x^{2}=35-5y^{2}\qquad/+5y^{2}$
$7x^{2}+5y^{2}=35\qquad/\div 35$
$\displaystyle \frac{x^{2}}{5}+\frac{y^{2}}{7}=1$
Major axis parallel to the $y$-axis, vertical.
$a=\sqrt{7}\approx 2.646$
$b=\sqrt{5}\approx 2.236$
Foci are $c$ units above and $c$ units below the center,
$c^{2}=a^{2}-b^{2}=7-5=2$
$c=\sqrt{2}\approx 1.414$
Foci:
$(0, -\sqrt{2})$ and $(0, \sqrt{2})$.
