Find the center, transverse axis, vertices, and foci of the hyperbola.
-$25 y ^ { 2 } - 36 x ^ { 2 } = 900$
A) center at $( 0,0 )$
transverse axis is $x$-axis
vertices: $( - 5,0 ) , ( 5,0 )$
foci: $( - \sqrt { 61 } , 0 ) , ( \sqrt { 61 } , 0 )$
B) center at $( 0,0 )$
transverse axis is $\mathrm { y }$-axis
vertices: $( 0 , - 6 ) , ( 0,6 )$
foci: $( - \sqrt { 61 } , 0 ) , ( \sqrt { 61 } , 0 )$
C) center at $( 0,0 )$
transverse axis is $x$-axis
vertices: $( - 6,0 ) , ( 6,0 )$
foci: $( - 5,0 ) , ( 5,0 )$
D) center at $( 0,0 )$
transverse axis is $y$-axis
vertices at $( 0 , - 6 )$ and $( 0,6 )$
foci at $( 0 , - \sqrt { 61 } )$ and $( 0 , \sqrt { 61 } )$

Question

Find the center, transverse axis, vertices, and foci of the hyperbola.
-$25 y ^ { 2 } - 36 x ^ { 2 } = 900$
A) center at $( 0,0 )$
transverse axis is $x$-axis
vertices: $( - 5,0 ) , ( 5,0 )$
foci: $( - \sqrt { 61 } , 0 ) , ( \sqrt { 61 } , 0 )$
B) center at $( 0,0 )$
 transverse axis is $\mathrm { y }$-axis
vertices: $( 0 , - 6 ) , ( 0,6 )$
foci: $( - \sqrt { 61 } , 0 ) , ( \sqrt { 61 } , 0 )$
C) center at $( 0,0 )$
transverse axis is $x$-axis
vertices: $( - 6,0 ) , ( 6,0 )$
foci: $( - 5,0 ) , ( 5,0 )$
D) center at $( 0,0 )$
transverse axis is $y$-axis
vertices at $( 0 , - 6 )$ and $( 0,6 )$
foci at $( 0 , - \sqrt { 61 } )$ and $( 0 , \sqrt { 61 } )$

Quizplus · Accepted Answer

The given equation is $25y^2 - 36x^2 = 900$, which can be rewritten as $\frac{y^2}{36} - \frac{x^2}{25} = 1$, indicating a hyperbola centered at (0,0) with its transverse axis along the y-axis. The vertices are at $(0, \pm6)$, and the foci, calculated using $c^2 = a^2 + b^2$, are at $(0, \pm\sqrt{61})$.

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