Find the vertices and foci of the ellipse.
-$36 x ^ { 2 } + 100 y ^ { 2 } = 3600$
A) Vertices: $( \pm 10,0 )$; Foci: $( \pm 8,0 )$
B) Vertices: $( \pm 36,0 )$; Foci: $( \pm 8,0 )$
C) Vertices: $( 0 , \pm 10 )$; Foci: $( 0 , \pm 8 )$
D) Vertices: $( 0 , \pm 36 )$; Foci: $( 0 , \pm 10 )$

Question

Quizplus · Accepted Answer

Dividing both sides by 3600, we get:
$$\frac{x^2}{100} + \frac{y^2}{36} = 1$$
This is the standard form of an ellipse centered at the origin. The vertices are given by $(\pm a, 0)$ and the foci are given by $(\pm c, 0)$, where $a$ and $c$ are the semi-major axis and the distance from the center to a focus, respectively. In this case, $a = 10$ and $c = 8$, so the vertices are $(\pm 10, 0)$ and the foci are $(\pm 8, 0)$. Therefore, the answer is A.

Find the Vertices and Foci of the Ellipse 36x2+100y2=360036 x ^ { 2 } + 100 y ^ { 2 } = 360036x2+100y2=3600

Find the Vertices and Foci of the Ellipse $36 x ^ { 2 } + 100 y ^ { 2 } = 3600$