Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola.
-$$\frac { y ^ { 2 } } { 36 } - \frac { x ^ { 2 } } { 81 } = 1$$
A) center at $( 0,0 )$
transverse axis is $\mathrm { y }$-axis
vertices: $( 0 , - 6 ) , ( 0,6 )$
foci: $( - 3 \sqrt { 13 } , 0 ) , ( 3 \sqrt { 13 } , 0 )$
asymptotes of $y = - \frac { 2 } { 3 } x$ and $y = \frac { 2 } { 3 } x$
B) center at $( 0,0 )$
transverse axis is $\mathrm { y }$-axis
vertices: $( 0 , - 6 ) , ( 0,6 )$
foci: $( 0 , - 3 \sqrt { 13 } ) , ( 0,3 \sqrt { 13 } )$
asymptotes of $y = - \frac { 2 } { 3 } x$ and $y = \frac { 2 } { 3 } x$
C) center at $( 0,0 )$
transverse axis is $\mathrm { x }$-axis
vertices: $( - 9,0 ) , ( 9,0 )$
foci: $( - 3 \sqrt { 13 } , 0 ) , ( 3 \sqrt { 13 } , 0 )$
asymptotes of $y = - \frac { 2 } { 3 } x$ and $y = \frac { 2 } { 3 } x$
D) center at $( 0,0 )$
transverse axis is $\mathrm { y }$-axis
vertices: $( - 6,0 ) , ( 6,0 )$
foci: $( - 9,0 ) , ( 9,0 )$
asymptotes of $y = - \frac { 2 } { 3 } x$ and $y = \frac { 2 } { 3 } x$

Question

Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola.
-$$\frac { y ^ { 2 } } { 36 } - \frac { x ^ { 2 } } { 81 } = 1$$
A) center at $( 0,0 )$
transverse axis is $\mathrm { y }$-axis
vertices: $( 0 , - 6 ) , ( 0,6 )$
foci: $( - 3 \sqrt { 13 } , 0 ) , ( 3 \sqrt { 13 } , 0 )$
asymptotes of $y = - \frac { 2 } { 3 } x$ and $y = \frac { 2 } { 3 } x$
B) center at $( 0,0 )$
 transverse axis is $\mathrm { y }$-axis
vertices: $( 0 , - 6 ) , ( 0,6 )$
foci: $( 0 , - 3 \sqrt { 13 } ) , ( 0,3 \sqrt { 13 } )$
asymptotes of $y = - \frac { 2 } { 3 } x$ and $y = \frac { 2 } { 3 } x$
C) center at $( 0,0 )$
transverse axis is $\mathrm { x }$-axis
vertices: $( - 9,0 ) , ( 9,0 )$
foci: $( - 3 \sqrt { 13 } , 0 ) , ( 3 \sqrt { 13 } , 0 )$
asymptotes of $y = - \frac { 2 } { 3 } x$ and $y = \frac { 2 } { 3 } x$
D) center at $( 0,0 )$
 transverse axis is $\mathrm { y }$-axis
vertices: $( - 6,0 ) , ( 6,0 )$
foci: $( - 9,0 ) , ( 9,0 )$
asymptotes of $y = - \frac { 2 } { 3 } x$ and $y = \frac { 2 } { 3 } x$

Quizplus · Accepted Answer

The equation of the hyperbola is given in the form $\frac{y^2}{a^2} - \frac{x^2}{b^2} = 1$, indicating that the transverse axis is along the y-axis. The center is at (0,0), vertices are at $(0, \pm a) = (0, \pm 6)$, foci are at $(0, \pm \sqrt{a^2 + b^2}) = (0, \pm \sqrt{36 + 81}) = (0, \pm 3\sqrt{13})$, and the asymptotes are given by $y = \pm \frac{a}{b}x = \pm \frac{6}{9}x = \pm \frac{2}{3}x$.

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