Find the Foci of the conic. $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 64 } = 1$
A)Foci: $( 0 , \pm \sqrt { 48 } )$
B)Foci: $( \pm \sqrt { 8 } , 0 )$
C)Foci: $( 0 , \pm \sqrt { 8 } )$
D)Foci: $( \pm \sqrt { 48 } , 0 )$
E)Foci: $( \sqrt { 8 } , \sqrt { 48 } )$

Question

Find the Foci of the conic.​ $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 64 } = 1$ ​
A)Foci: $( 0 , \pm \sqrt { 48 } )$
B)Foci: $( \pm \sqrt { 8 } , 0 )$
C)Foci: $( 0 , \pm \sqrt { 8 } )$
D)Foci: $( \pm \sqrt { 48 } , 0 )$
E)Foci: $( \sqrt { 8 } , \sqrt { 48 } )$

Quizplus · Accepted Answer

The given conic is a hyperbola, which has two foci. Using the formula for the foci of a hyperbola, the coordinates of the foci can be calculated as (0, ±√3). Therefore, the correct choice is A), which matches these coordinates. The other choices have different coordinates that do not match those of the foci of the given hyperbola.

Find the Foci of the Conic x216+y264=1\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 64 } = 116x2​+64y2​=1

Find the Foci of the Conic $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 64 } = 1$