Find the center, vertices, and foci of the ellipse below.
$$x ^ { 2 } + 8 y ^ { 2 } = 80$$

A) Center: $( 0,0 )$
Vertices: $( 4 \sqrt { 5 } , 0 ) , ( - 4 \sqrt { 5 } , 0 )$
Foci: $( \sqrt { 70 } , 0 ) , ( - \sqrt { 70 } , 0 )$

B) Center: $( 0,0 )$
Vertices: $( 0,10 ) , ( 0 , - 10 )$
Foci: $( 0,24 \sqrt { 11 } ) , ( 0 , - 24 \sqrt { 11 } )$

C)Center: $( 80,10 )$
Vertices: $( 160,10 ) , ( - 160,10 )$
Foci: $( 80 + 24 \sqrt { 11 } , 10 ) , ( 80 - 24 \sqrt { 11 } , 10 )$

D)Center: $( 80,10 )$
Vertices: $( 80,20 ) , ( 80 , - 20 )$
Foci: $( 80,10 + 24 \sqrt { 11 } ) , ( 80,10 - 24 \sqrt { 11 } )$

E)Center: $( 0,0 )$
Vertices: $( 80,0 ) , ( - 80,0 )$
Foci: $( 6336,0 ) , ( - 6336,0 )$

Question

Find the center, vertices, and foci of the ellipse below.
$$x ^ { 2 } + 8 y ^ { 2 } = 80$$

A) Center: $( 0,0 )$
Vertices: $( 4 \sqrt { 5 } , 0 ) , ( - 4 \sqrt { 5 } , 0 )$
Foci: $( \sqrt { 70 } , 0 ) , ( - \sqrt { 70 } , 0 )$

B) Center: $( 0,0 )$
Vertices: $( 0,10 ) , ( 0 , - 10 )$
Foci: $( 0,24 \sqrt { 11 } ) , ( 0 , - 24 \sqrt { 11 } )$

C)Center: $( 80,10 )$
 Vertices: $( 160,10 ) , ( - 160,10 )$
Foci: $( 80 + 24 \sqrt { 11 } , 10 ) , ( 80 - 24 \sqrt { 11 } , 10 )$

D)Center: $( 80,10 )$
 Vertices: $( 80,20 ) , ( 80 , - 20 )$
Foci: $( 80,10 + 24 \sqrt { 11 } ) , ( 80,10 - 24 \sqrt { 11 } )$

E)Center: $( 0,0 )$
 Vertices: $( 80,0 ) , ( - 80,0 )$
Foci: $( 6336,0 ) , ( - 6336,0 )$

Quizplus · Accepted Answer

We recognize that this ellipse is in standard form, where $a = 4\sqrt{5}$ and $b = \sqrt{10}$. Thus, the center is at the origin $(0,0)$, the vertices are at $(\pm a, 0) = (\pm 4\sqrt{5}, 0)$, and the foci are at $(\pm c, 0)$ where $c = \sqrt{a^2 - b^2} = \sqrt{70}$. Hence, the foci are at $(\pm\sqrt{70}, 0)$.

Find the Center, Vertices, and Foci of the Ellipse Below x2+8y2=80x ^ { 2 } + 8 y ^ { 2 } = 80x2+8y2=80

Find the Center, Vertices, and Foci of the Ellipse Below $x ^ { 2 } + 8 y ^ { 2 } = 80$