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

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

Quizplus · Accepted Answer

The given equation can be rewritten as $\frac{y^2}{4} + \frac{x^2}{2} = 1$, which is the standard form of an ellipse centered at the origin with vertical major axis. The vertices are at $(0, \pm 2)$ and the foci are at $(0, \pm \sqrt{2})$.

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 $y ^ { 2 } = 4 - 2 x ^ { 2 }$