Find the vertices and foci for the ellipse. $y ^ { 2 } = 4 - 2 x ^ { 2 }$
A)Vertices: $( 0 , \pm \sqrt { 2 } )$
, foci: $( 0 , \pm 2 )$
B)Vertices: $( \pm 2,0 )$
, foci: $( 0 , \pm \sqrt { 2 } )$
C)Vertices: $( 0 , \pm 2 )$
, foci: $( 0 , \pm \sqrt { 2 } )$
D)Vertices: $( 0 , \pm 2 )$
, foci: $( \pm \sqrt { 2 } , 0 )$
E) none of these

Question

Quizplus · Accepted Answer

We can rewrite the equation as $\frac{x^2}{1}+\frac{y^2}{\frac{4}{2}}=1$. This is the equation of an ellipse centered at the origin with semi-major axis of length 2 and semi-minor axis of length $\sqrt{2}$. Thus, the vertices are at $(0,\pm 2)$ and the foci are at $(0,\pm\sqrt{2})$. The only answer choice that matches this is $\boxed{	extbf{(C)}}$.

Find the Vertices and Foci for the Ellipse y2=4−2x2y ^ { 2 } = 4 - 2 x ^ { 2 }y2=4−2x2

Find the Vertices and Foci for the Ellipse $y ^ { 2 } = 4 - 2 x ^ { 2 }$