Answer
Foci:
$(0,-\displaystyle \frac{\sqrt{3}}{2})$ and $(0, \displaystyle \frac{\sqrt{3}}{2})$.
Work Step by Step
Write the equation in standard form:
$y^{2}=1-4x^{2}\qquad/+4x^{2}$
$4x^{2}+y^{2}=1$
$\displaystyle \frac{x^{2}}{\frac{1}{4}}+\frac{y^{2}}{1}=1$
Major axis parallel to the $y$-axis, vertical.
$a=1, \ \ \ b=\displaystyle \frac{1}{2}.$
Vertices: $(h, k-a),\quad (h, k+a) $
$(0, -1),\quad (0, 1) $
Foci are $c$ units above and $c$ units below the center,
$c^{2}=a^{2}-b^{2}=1-\displaystyle \frac{1}{4}=\frac{3}{4}$
$c=\displaystyle \frac{\sqrt{3}}{2}$
Foci:
$(0,-\displaystyle \frac{\sqrt{3}}{2})$ and $(0, \displaystyle \frac{\sqrt{3}}{2})$.
