Answer
$\displaystyle \frac{x^{2}}{2}+y^{2}=1,$
Foci: $\quad(\pm 1, 0)$
Vertices: $\quad (\pm\sqrt{2}, 0)$
Work Step by Step
Ellipse, horizontal major axis.
Foci on the x-axis: $\quad \displaystyle \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 \quad (a\gt b)$
Center-to-focus distance: $c=\sqrt{a^{2}-b^{2}}$
Foci: $\quad(\pm c, 0)$
Vertices: $\quad (\pm a, 0)$
Of the offered equations, $\quad \displaystyle \frac{x^{2}}{2}+\frac{y^{2}}{1}=1 \quad (a=\sqrt{2}$ ,$b=1 )$
Center-to-focus distance: $c=\sqrt{2-1}=1$
Foci: $\quad(\pm 1, 0)$
Vertices: $\quad (\pm\sqrt{2}, 0)$
