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

Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola.
- $25 y ^ { 2 } - 16 x ^ { 2 } = 400$

A) center at $( 0,0 )$
transverse axis is $x$ -axis
vertices: $( - 5,0 ) , ( 5,0 )$
foci: $( - \sqrt { 41 } , 0 ) , ( \sqrt { 41 } , 0 )$
asymptotes of $y = - \frac { 4 } { 5 }$ and $y = \frac { 4 } { 5 }$

B) center at $( 0,0 )$
transverse axis is $x$ -axis
vertices: $( - 4,0 ) , ( 4,0 )$
foci: $( - 5,0 ) , ( 5,0 )$
asymptotes of $y = - \frac { 4 } { 5 }$ and $y = \frac { 4 } { 5 }$

C) center at $( 0,0 )$
transverse axis is $y$ -axis
vertices: $( 0 , - 4 ) , ( 0,4 )$
foci: $( - \sqrt { 41 } , 0 ) , ( \sqrt { 41 } , 0 )$
asymptotes of $y = - \frac { 4 } { 5 }$ and $y = \frac { 4 } { 5 }$

D) center at $( 0,0 )$
transverse axis is y-axis
vertices at $( 0 , - 4 )$ and $( 0,4 )$
foci at $( 0 , - \sqrt { 41 } )$ and $( 0 , \sqrt { 41 } )$
asymptotes of $\mathrm { y } = - \frac { 4 } { 5 }$ and $\mathrm { y } = \frac { 4 } { 5 }$

Correct Answer:

Verified

Unlock this answer now
Get Access to more Verified Answers free of charge

Access For Free