Find the center, transverse axis, vertices, and foci of the hyperbola.
-$$16 x ^ { 2 } - 100 y ^ { 2 } = 1600$$
A) center at $( 0,0 )$
transverse axis is $x$-axis
vertices: $( 0 , - 10 ) , ( 0,10 )$
foci: $( 0 , - 2 \sqrt { 29 } ) , ( 0,2 \sqrt { 29 } )$
B) center at $( 0,0 )$
transverse axis is $x$-axis
vertices: $( - 10,0 ) , ( 10,0 )$
foci: $( - 2 \sqrt { 21 } , 0 ) , ( 2 \sqrt { 21 } , 0 )$
C) center at $( 0,0 )$
transverse axis is $x$-axis
vertices: $( - 4,0 ) , ( 4,0 )$
foci: $( - 2 \sqrt { 29 } , 0 ) , ( 2 \sqrt { 29 } , 0 )$
D) center at $( 0,0 )$
transverse axis is $\mathrm { x }$-axis
vertices: $( - 10,0 ) , ( 10,0 )$
foci: $( - 2 \sqrt { 29 } , 0 ) , ( 2 \sqrt { 29 } , 0 )$

Question

Quizplus · Accepted Answer

The given equation can be rewritten as $\frac{x^2}{100} - \frac{y^2}{16} = 1$, which is a hyperbola centered at $(0,0)$ with the transverse axis along the $x$-axis. The vertices are at $(\pm 10, 0)$ and the foci are at $(\pm 2\sqrt{29}, 0)$.

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