Find the vertices and foci of the ellipse.
-$$4 x ^ { 2 } + 25 y ^ { 2 } = 100$$
A) Vertices: $( \pm 5,0 )$; Foci: $( \pm \sqrt { 21 } , 0 )$
B) Vertices: $( 0 , \pm 2 )$; Foci $( 0 , \pm \sqrt { 21 } )$
C) Vertices: $( \pm 2,0 )$; Foci: $( \pm \sqrt { 21 } , 0 )$
D) Vertices: $( 0 , \pm 5 )$; Foci $( 0 , \pm \sqrt { 21 } )$

Question

Quizplus · Accepted Answer

The given equation is in the form $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ with $a^2 = 25$ and $b^2 = 4$, indicating the major axis is along the x-axis. Thus, vertices are $(\pm \sqrt{25}, 0) = (\pm 5, 0)$ and foci are $(\pm \sqrt{a^2 - b^2}, 0) = (\pm \sqrt{25 - 4}, 0) = (\pm \sqrt{21}, 0)$.

Find the Vertices and Foci of the Ellipse 4x2+25y2=1004 x ^ { 2 } + 25 y ^ { 2 } = 1004x2+25y2=100

Find the Vertices and Foci of the Ellipse $4 x ^ { 2 } + 25 y ^ { 2 } = 100$