Find the center and foci of the ellipse. $\frac { ( x + 1 ) ^ { 2 } } { 7 } + \frac { ( y - 5 ) ^ { 2 } } { 16 } = 1$
A)center: $( 1 , - 5 )$ foci: $( 1,4 ) , ( 1 , - 2 )$
B)center: $( - 1,5 )$ foci: $( 8,5 ) , ( 2,5 )$
C)center: $( - 1,5 )$ foci: $( - 1,2 ) , ( - 1,8 )$
D)center: $( - 1,5 )$ foci: $( - 2 , - 5 ) , ( 4 , - 5 )$
E)center: $( 1 , - 5 )$ foci: $( - 2,5 ) , ( 4,5 )$

Question

Find the center and foci of the ellipse.​ $\frac { ( x + 1 ) ^ { 2 } } { 7 } + \frac { ( y - 5 ) ^ { 2 } } { 16 } = 1$ ​
A)center: $( 1 , - 5 )$ foci: $( 1,4 ) , ( 1 , - 2 )$
B)center: $( - 1,5 )$ foci: $( 8,5 ) , ( 2,5 )$
C)center: $( - 1,5 )$ foci: $( - 1,2 ) , ( - 1,8 )$
D)center: $( - 1,5 )$ foci: $( - 2 , - 5 ) , ( 4 , - 5 )$
E)center: $( 1 , - 5 )$ foci: $( - 2,5 ) , ( 4,5 )$

Quizplus · Accepted Answer

The center of the ellipse is found by setting the inside of the parentheses to zero, giving $(-1, 5)$. The distance of the foci from the center along the y-axis is $c = \sqrt{16 - 7} = 3$, so the foci are at $(-1, 5 \pm 3)$, which simplifies to $(-1, 2)$ and $(-1, 8)$.

Find the Center and Foci of the Ellipse (x+1)27+(y−5)216=1\frac { ( x + 1 ) ^ { 2 } } { 7 } + \frac { ( y - 5 ) ^ { 2 } } { 16 } = 17(x+1)2​+16(y−5)2​=1

Find the Center and Foci of the Ellipse $\frac { ( x + 1 ) ^ { 2 } } { 7 } + \frac { ( y - 5 ) ^ { 2 } } { 16 } = 1$