The Hyperbola
1 Locate a Hyperbola's Vertices and Foci
-$\frac { y ^ { 2 } } { 100 } - \frac { x ^ { 2 } } { 81 } = 1$
A) vertices: $( 0 , - 10 ) , ( 0,10 )$
foci: $( 0 , - \sqrt { 181 } ) , ( 0 , \sqrt { 181 } )$
B) vertices: $( - 9,0 ) , ( 9,0 )$
foci: $( - \sqrt { 181 } , 0 ) , ( \sqrt { 181 } , 0 )$
C) vertices: $( 0 , - 10 ) , ( 0,10 )$
foci: $( - \sqrt { 181 } , 0 ) , ( \sqrt { 181 } , 0 )$

D) vertices: $( - 10,0 ) , ( 10,0 )$
foci: $( - 9,0 ) , ( 9,0 )$

Question

The Hyperbola
1 Locate a Hyperbola's Vertices and Foci
-$\frac { y ^ { 2 } } { 100 } - \frac { x ^ { 2 } } { 81 } = 1$
A) vertices: $( 0 , - 10 ) , ( 0,10 )$
 foci: $( 0 , - \sqrt { 181 } ) , ( 0 , \sqrt { 181 } )$
B) vertices: $( - 9,0 ) , ( 9,0 )$
 foci: $( - \sqrt { 181 } , 0 ) , ( \sqrt { 181 } , 0 )$
C) vertices: $( 0 , - 10 ) , ( 0,10 )$
foci: $( - \sqrt { 181 } , 0 ) , ( \sqrt { 181 } , 0 )$

D) vertices: $( - 10,0 ) , ( 10,0 )$
 foci: $( - 9,0 ) , ( 9,0 )$

Quizplus · Accepted Answer

The given equation $\frac { y ^ { 2 } } { 100 } - \frac { x ^ { 2 } } { 81 } = 1$ represents a hyperbola centered at the origin with its major axis along the y-axis. The vertices are at $(0, \pm 10)$, and the foci are at $(0, \pm \sqrt{181})$, as calculated using the formula $c^2 = a^2 + b^2$, where $c$ is the distance from the center to a focus, $a$ is the distance from the center to a vertex, and $b$ is the distance from the center to the ends of the minor axis.

The Hyperbola 1 Locate a Hyperbola's Vertices and Foci - y2100−x281=1\frac { y ^ { 2 } } { 100 } - \frac { x ^ { 2 } } { 81 } = 1100y2​−81x2​=1

The Hyperbola
1 Locate a Hyperbola's Vertices and Foci
- $\frac { y ^ { 2 } } { 100 } - \frac { x ^ { 2 } } { 81 } = 1$