Find the vertices and foci of the ellipse.
-$$\frac { x ^ { 2 } } { 225 } + \frac { y ^ { 2 } } { 625 } = 1$$
A) Vertices: $( 0 , \pm 25 )$; Foci: $( 0 , \pm 20 )$
B) Vertices: $( \pm 15,0 )$; Foci: $( \pm 20,0 )$
C) Vertices: $( 0 , \pm 25 )$; Foci: $( 0 , \pm 15 )$
D) Vertices: $( \pm 25,0 )$; Foci: $( \pm 15,0 )$

Question

Quizplus · Accepted Answer

The given equation of the ellipse is $\frac{x^2}{225} + \frac{y^2}{625} = 1$, which is in the form $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$, where $a^2 = 225$ and $b^2 = 625$. Since $b^2 > a^2$, the major axis is along the y-axis. The vertices are at $(0, \pm b)$, so $(0, \pm 25)$. The foci are at $(0, \pm c)$, where $c = \sqrt{b^2 - a^2} = \sqrt{625 - 225} = \sqrt{400} = 20$. Therefore, the foci are at $(0, \pm 20)$.

Find the Vertices and Foci of the Ellipse x2225+y2625=1\frac { x ^ { 2 } } { 225 } + \frac { y ^ { 2 } } { 625 } = 1225x2​+625y2​=1

Find the Vertices and Foci of the Ellipse $\frac { x ^ { 2 } } { 225 } + \frac { y ^ { 2 } } { 625 } = 1$