Find the center, transverse axis, vertices, and foci of the hyperbola.
-$$\frac { x ^ { 2 } } { 121 } - \frac { y ^ { 2 } } { 25 } = 1$$
A) center at $( 0,0 )$
transverse axis is $y$-axis
vertices at $( 0 , - 11 )$ and $( 0,11 )$
foci at $( - \sqrt { 146 } , 0 )$ and $( \sqrt { 146 } , 0 )$
B) center at $( 0,0 )$
transverse axis is $\mathrm { x }$-axis
vertices at $( - 11,0 )$ and $( 11,0 )$
foci at $( - 5,0 )$ and $( 5,0 )$
C) center at $( 0,0 )$
transverse axis is $x$-axis
vertices at $( - 5,0 )$ and $( 5,0 )$
foci at $( - \sqrt { 146 } , 0 )$ and $( \sqrt { 146 } , 0 )$
D) center at $( 0,0 )$
transverse axis is $x$-axis
vertices at $( - 11,0 )$ and $( 11,0 )$
foci at $( - \sqrt { 146 } , 0 )$ and $( \sqrt { 146 } , 0 )$

Question

Find the center, transverse axis, vertices, and foci of the hyperbola.
-$$\frac { x ^ { 2 } } { 121 } - \frac { y ^ { 2 } } { 25 } = 1$$
A) center at $( 0,0 )$
transverse axis is $y$-axis
vertices at $( 0 , - 11 )$ and $( 0,11 )$
foci at $( - \sqrt { 146 } , 0 )$ and $( \sqrt { 146 } , 0 )$
B) center at $( 0,0 )$
 transverse axis is $\mathrm { x }$-axis
vertices at $( - 11,0 )$ and $( 11,0 )$
foci at $( - 5,0 )$ and $( 5,0 )$
C) center at $( 0,0 )$
transverse axis is $x$-axis 
vertices at $( - 5,0 )$ and $( 5,0 )$
foci at $( - \sqrt { 146 } , 0 )$ and $( \sqrt { 146 } , 0 )$
D) center at $( 0,0 )$
transverse axis is $x$-axis 
vertices at $( - 11,0 )$ and $( 11,0 )$
foci at $( - \sqrt { 146 } , 0 )$ and $( \sqrt { 146 } , 0 )$

Quizplus · Accepted Answer

The equation of the hyperbola is given in the form $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$, indicating that the transverse axis is along the x-axis. The center is at (0,0), vertices are $a$ units from the center along the x-axis ($a = 11$), and the foci are $\sqrt{a^2 + b^2}$ units from the center along the x-axis, where $a^2 = 121$ and $b^2 = 25$, so $\sqrt{a^2 + b^2} = \sqrt{146}$.

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