The Hyperbola
1 Locate a Hyperbola's Vertices and Foci
-$$\frac { x ^ { 2 } } { 64 } - \frac { y ^ { 2 } } { 16 } = 1$$
A) vertices: $( - 8,0 ) , ( 8,0 )$
B) vertices: $( - 4,0 ) , ( 4,0 )$
foci: $( - 4 \sqrt { 5 } , 0 ) , ( 4 \sqrt { 5 } , 0 )$
foci: $( - 4 \sqrt { 5 } , 0 ) , ( 4 \sqrt { 5 } , 0 )$
C) vertices: $( 0 , - 8 ) , ( 0,8 )$
D) vertices: $( - 8,0 ) , ( 8,0 )$
foci: $( - 4 \sqrt { 5 } , 0 ) , ( 4 \sqrt { 5 } , 0 )$
foci: $( - 4,0 ) , ( 4,0 )$

Question

Quizplus · Accepted Answer

The equation of the hyperbola is in the form $\frac { x ^ { 2 } } { a ^ { 2 } } - \frac { y ^ { 2 } } { b ^ { 2 } } = 1$, where $a$ is the distance from the center to the vertices and $b$ is the distance from the center to the foci. In this case, $a = 8$ and $b = 4$, so the vertices are $( - 8,0 )$ and $( 8,0 )$, and the foci are $( - 4 \sqrt { 5 } , 0 )$ and $( 4 \sqrt { 5 } , 0 )$.

The Hyperbola 1 Locate a Hyperbola's Vertices and Foci - x264−y216=1\frac { x ^ { 2 } } { 64 } - \frac { y ^ { 2 } } { 16 } = 164x2​−16y2​=1

The Hyperbola
1 Locate a Hyperbola's Vertices and Foci
- $\frac { x ^ { 2 } } { 64 } - \frac { y ^ { 2 } } { 16 } = 1$