Find the center, foci, and vertices of the ellipse.
-$16 x ^ { 2 } + y ^ { 2 } - 256 x + 1,008 = 0$
A) $( x - 2 ) ^ { 2 } + \frac { y ^ { 2 } } { 64 } = 1$
center: $( 2,0 )$; foci: $( 2,3 \sqrt { 7 } ) , ( 2 , - 3 \sqrt { 7 } )$; vertices: $( 2,8 ) , ( 2 , - 8 )$

B) $( x - 8 ) ^ { 2 } + \frac { y ^ { 2 } } { 4 } = 1$
center: $( 8,0 )$; foci: $( 8 , \sqrt { 3 } ) , ( 8 , - \sqrt { 3 } )$; vertices: $( 8,2 ) , ( 8 , - 2 )$

C) $\frac { x ^ { 2 } } { 64 } + ( y - 2 ) ^ { 2 } = 1$
center: $( 2,0 )$; foci: $( 2,3 \sqrt { 7 } ) , ( 2 , - 3 \sqrt { 7 } )$; vertices: $( 2,8 ) , ( 2 , - 8 )$

D) $\frac { x ^ { 2 } } { 4 } + ( y - 8 ) ^ { 2 } = 1$
center: $( 8,0 )$; foci: $( 8 , \sqrt { 3 } ) , ( 8 , - 3 \sqrt { 7 } )$; vertices: $( 8,2 )$,
$( 8 , - 2 )$

Question

Find the center, foci, and vertices of the ellipse.
-$16 x ^ { 2 } + y ^ { 2 } - 256 x + 1,008 = 0$
A) $( x - 2 ) ^ { 2 } + \frac { y ^ { 2 } } { 64 } = 1$
center: $( 2,0 )$; foci: $( 2,3 \sqrt { 7 } ) , ( 2 , - 3 \sqrt { 7 } )$; vertices: $( 2,8 ) , ( 2 , - 8 )$

B) $( x - 8 ) ^ { 2 } + \frac { y ^ { 2 } } { 4 } = 1$
center: $( 8,0 )$; foci: $( 8 , \sqrt { 3 } ) , ( 8 , - \sqrt { 3 } )$; vertices: $( 8,2 ) , ( 8 , - 2 )$

C) $\frac { x ^ { 2 } } { 64 } + ( y - 2 ) ^ { 2 } = 1$
center: $( 2,0 )$; foci: $( 2,3 \sqrt { 7 } ) , ( 2 , - 3 \sqrt { 7 } )$; vertices: $( 2,8 ) , ( 2 , - 8 )$

D) $\frac { x ^ { 2 } } { 4 } + ( y - 8 ) ^ { 2 } = 1$
center: $( 8,0 )$; foci: $( 8 , \sqrt { 3 } ) , ( 8 , - 3 \sqrt { 7 } )$; vertices: $( 8,2 )$,
$( 8 , - 2 )$

Quizplus · Accepted Answer

The given equation can be rewritten as:$$16(x-8)^2+y^2=1024$$Dividing both sides by 1024, we get:$$\frac{(x-8)^2}{64}+\frac{y^2}{1024}=1$$Therefore, the center of the ellipse is (8,0), the foci are (8,±3√7), and the vertices are (8,±8).

Find the Center, Foci, and Vertices of the Ellipse 16x2+y2−256x+1,008=016 x ^ { 2 } + y ^ { 2 } - 256 x + 1,008 = 016x2+y2−256x+1,008=0

Find the Center, Foci, and Vertices of the Ellipse $16 x ^ { 2 } + y ^ { 2 } - 256 x + 1,008 = 0$