Find the vertices and locate the foci for the hyperbola whose equation is given.
-$$\frac { y ^ { 2 } } { 100 } - \frac { x ^ { 2 } } { 121 } = 1$$
A) vertices: $( 0 , - 10 ) , ( 0,10 )$
foci: $( 0 , - \sqrt { 221 } ) , ( 0 , \sqrt { 221 } )$
B) vertices: $( - 11,0 ) , ( 11,0 )$
foci: $( - \sqrt { 221 } , 0 ) , ( \sqrt { 221 } , 0 )$
C) vertices: $( 0 , - 10 ) , ( 0,10 )$
foci: $( - \sqrt { 221 } , 0 ) , ( \sqrt { 221 } , 0 )$
D) vertices: $( - 10,0 ) , ( 10,0 )$
foci: $( - 11,0 ) , ( 11,0 )$

Question

Find the vertices and locate the foci for the hyperbola whose equation is given.
-$$\frac { y ^ { 2 } } { 100 } - \frac { x ^ { 2 } } { 121 } = 1$$
A) vertices: $( 0 , - 10 ) , ( 0,10 )$
 foci: $( 0 , - \sqrt { 221 } ) , ( 0 , \sqrt { 221 } )$
B) vertices: $( - 11,0 ) , ( 11,0 )$
foci: $( - \sqrt { 221 } , 0 ) , ( \sqrt { 221 } , 0 )$
C) vertices: $( 0 , - 10 ) , ( 0,10 )$
foci: $( - \sqrt { 221 } , 0 ) , ( \sqrt { 221 } , 0 )$
D) vertices: $( - 10,0 ) , ( 10,0 )$
foci: $( - 11,0 ) , ( 11,0 )$

Quizplus · Accepted Answer

The given equation is of a hyperbola centered at the origin with the y-term positive and leading, indicating that the transverse axis is vertical. The vertices are found at $(0, \pm\sqrt{100}) = (0, \pm10)$, and the foci are located along the same axis as the vertices, calculated using $c = \sqrt{a^2 + b^2} = \sqrt{100 + 121} = \sqrt{221}$, resulting in foci at $(0, -\sqrt{221}), (0, \sqrt{221})$.

Find the Vertices and Locate the Foci for the Hyperbola y2100−x2121=1\frac { y ^ { 2 } } { 100 } - \frac { x ^ { 2 } } { 121 } = 1100y2​−121x2​=1

Find the Vertices and Locate the Foci for the Hyperbola $\frac { y ^ { 2 } } { 100 } - \frac { x ^ { 2 } } { 121 } = 1$