Find the center, foci, and vertices of the ellipse.
-$$36 x ^ { 2 } + 9 y ^ { 2 } = 324$$
A) center at $( 0,0 )$
foci at $( - 3 \sqrt { 3 } , 0 )$ and $( 3 \sqrt { 3 } , 0 )$
vertices at $( - 6,0 ) , ( 6,0 )$
B) center at $( 0,0 )$
foci at $( 0 , - 6 )$ and $( 0,6 )$
vertices at $( 0 , - 36 ) , ( 0,36 )$
C) center at $( 0,0 )$
foci at $( 0 , - 3 \sqrt { 3 } )$ and $( 0,3 \sqrt { 3 } )$
vertices at $( 0 , - 6 ) , ( 0,6 )$
D) center at $( 0,0 )$
foci at $( 0,6 )$ and $( 3,0 )$
vertices at $( 0,36 )$ and $( 9,0 )$

Question

Quizplus · Accepted Answer

The equation can be rewritten as $\frac{x^2}{9} + \frac{y^2}{36} = 1$, indicating a vertical ellipse centered at (0,0) with semi-major axis 6 and semi-minor axis 3. The foci are at $(0, \pm 3\sqrt{3})$ and the vertices are at $(0, \pm 6)$.

Find the Center, Foci, and Vertices of the Ellipse 36x2+9y2=32436 x ^ { 2 } + 9 y ^ { 2 } = 32436x2+9y2=324

Find the Center, Foci, and Vertices of the Ellipse $36 x ^ { 2 } + 9 y ^ { 2 } = 324$