Find the center, transverse axis, vertices, and foci of the hyperbola.
-$$\frac { y ^ { 2 } } { 4 } - \frac { x ^ { 2 } } { 121 } = 1$$
A) center at $( 0,0 )$
transverse axis is $\mathrm { y }$-axis
vertices: $( 0 , - 2 ) , ( 0,2 )$
oci: $( 0 , - 5 \sqrt { 5 } ) , ( 0,5 \sqrt { 5 } )$
B) center at $( 0,0 )$
transverse axis is $y$-axis
vertices: $( - 2,0 ) , ( 2,0 )$ f
foci: $( - 11,0 ) , ( 11,0 )$
C) center at $( 0,0 )$
transverse axis is $y$-axis
vertices: $( 0 , - 2 ) , ( 0,2 )$
foci: $( - 5 \sqrt { 5 } , 0 ) , ( 5 \sqrt { 5 } , 0 )$
D) center at $( 0,0 )$
transverse axis is $x$-axis
vertices: $( - 11,0 ) , ( 11,0 )$
foci: $( - 5 \sqrt { 5 } , 0 ) , ( 5 \sqrt { 5 } , 0 )$

Question

Find the center, transverse axis, vertices, and foci of the hyperbola.
-$$\frac { y ^ { 2 } } { 4 } - \frac { x ^ { 2 } } { 121 } = 1$$
A) center at $( 0,0 )$
transverse axis is $\mathrm { y }$-axis
vertices: $( 0 , - 2 ) , ( 0,2 )$ 
oci: $( 0 , - 5 \sqrt { 5 } ) , ( 0,5 \sqrt { 5 } )$
B) center at $( 0,0 )$
 transverse axis is $y$-axis 
vertices: $( - 2,0 ) , ( 2,0 )$ f
foci: $( - 11,0 ) , ( 11,0 )$
C) center at $( 0,0 )$
transverse axis is $y$-axis
 vertices: $( 0 , - 2 ) , ( 0,2 )$
foci: $( - 5 \sqrt { 5 } , 0 ) , ( 5 \sqrt { 5 } , 0 )$
D) center at $( 0,0 )$
 transverse axis is $x$-axis 
vertices: $( - 11,0 ) , ( 11,0 )$
foci: $( - 5 \sqrt { 5 } , 0 ) , ( 5 \sqrt { 5 } , 0 )$

Quizplus · Accepted Answer

The given equation $\frac { y ^ { 2 } } { 4 } - \frac { x ^ { 2 } } { 121 } = 1$ indicates a hyperbola centered at $(0,0)$ with a vertical transverse axis because the $y^2$ term is positive. The vertices are $(0, \pm 2)$ because the square root of 4 is 2, and the foci are $(0, \pm \sqrt{4 + 121}) = (0, \pm \sqrt{125}) = (0, \pm 5\sqrt{5})$, following the formula $c = \sqrt{a^2 + b^2}$.

Find the Center, Transverse Axis, Vertices, and Foci of the Hyperbola