Find the center, foci, and vertices of the ellipse.
-$$\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 9 } = 1$$
A) center at $( 0,0 )$
foci at $( - 6 \sqrt { 2 } , 0 )$ and $( 6 \sqrt { 2 } , 0 )$
vertices at $( - 9,0 ) , ( 9,0 )$

B) center at $( 0,0 )$
foci at $( 0 , - 3 )$ and $( 0,3 )$
vertices at $( 0 , - 9 ) , ( 0,9 )$

C) center at $( 0,0 )$
foci at $( 0 , - 6 \sqrt { 2 } )$ and $( 0,6 \sqrt { 2 } )$
vertices at $( 0 , - 9 ) , ( 0,9 )$

D) center at $( 0,0 )$
foci at $( - 9,0 )$ and $( 9,0 )$
vertice at $( - 81,0 ) , ( 81,0 )$

Question

Find the center, foci, and vertices of the ellipse.
-$$\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 9 } = 1$$
A) center at $( 0,0 )$
foci at $( - 6 \sqrt { 2 } , 0 )$ and $( 6 \sqrt { 2 } , 0 )$
vertices at $( - 9,0 ) , ( 9,0 )$

B) center at $( 0,0 )$
foci at $( 0 , - 3 )$ and $( 0,3 )$
vertices at $( 0 , - 9 ) , ( 0,9 )$

C) center at $( 0,0 )$
foci at $( 0 , - 6 \sqrt { 2 } )$ and $( 0,6 \sqrt { 2 } )$
vertices at $( 0 , - 9 ) , ( 0,9 )$

D) center at $( 0,0 )$
foci at $( - 9,0 )$ and $( 9,0 )$
vertice at $( - 81,0 ) , ( 81,0 )$

Quizplus · Accepted Answer

The center of the ellipse is at the origin (0,0) because there are no shifts in the equation. The major axis is along the x-axis because the larger denominator is under $x^2$, making the vertices at $(-9,0)$ and $(9,0)$. The distance between the center and the foci is $c=\sqrt{a^2-b^2}=\sqrt{81-9}=\sqrt{72}=6\sqrt{2}$, placing the foci at $(-6\sqrt{2},0)$ and $(6\sqrt{2},0)$.

Find the Center, Foci, and Vertices of the Ellipse x281+y29=1\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 9 } = 181x2​+9y2​=1

Find the Center, Foci, and Vertices of the Ellipse $\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 9 } = 1$