Identify the vertices and asymptotes of the hyperbola. y 2 49 − x 2 100 = 1 \frac { y ^ { 2 } } { 49 } - \frac { x ^ { 2 } } { 100 } = 1 49 y 2 − 100 x 2 = 1 A) vertices: ( − 10 , 0 ) , ( 10 , 0 ) ( - 10,0 ) , ( 10,0 ) ( − 10 , 0 ) , ( 10 , 0 ) asymptotes: y = − 7 10 x , y = 7 10 x y = - \frac { 7 } { 10 } x , y = \frac { 7 } { 10 } x y = − 10 7 x , y = 10 7 x B) vertices: ( − 10 , 0 ) , ( 10 , 0 ) ( - 10,0 ) , ( 10,0 ) ( − 10 , 0 ) , ( 10 , 0 ) asymptotes: y = − 10 7 x , y = 10 7 x y = - \frac { 10 } { 7 } x , y = \frac { 10 } { 7 } x y = − 7 10 x , y = 7 10 x C) vertices: ( 0 , − 7 ) , ( 0 , 7 ) ( 0 , - 7 ) , ( 0,7 ) ( 0 , − 7 ) , ( 0 , 7 ) asymptotes: y = − 7 10 x , y = 7 10 x y = - \frac { 7 } { 10 } x , y = \frac { 7 } { 10 } x y = − 10 7 x , y = 10 7 x D) vertices: ( 0 , − 10 ) , ( 0 , 10 ) ( 0 , - 10 ) , ( 0,10 ) ( 0 , − 10 ) , ( 0 , 10 ) asymptotes: y = − 7 10 x , y = 7 10 x y = - \frac { 7 } { 10 } x , y = \frac { 7 } { 10 } x y = − 10 7 x , y = 10 7 x E) vertices: ( − 7 , 0 ) , ( 7 , 0 ) ( - 7,0 ) , ( 7,0 ) ( − 7 , 0 ) , ( 7 , 0 ) asymptotes: y = − 10 7 x , y = 10 7 x y = - \frac { 10 } { 7 } x , y = \frac { 10 } { 7 } x y = − 7 10 x , y = 7 10 x

Question

Identify the vertices and asymptotes of the hyperbola.   y 2 49 − x 2 100 = 1 \frac { y ^ { 2 } } { 49 } - \frac { x ^ { 2 } } { 100 } = 1 49 y 2 ​ − 100 x 2 ​ = 1 A) vertices:   ( − 10 , 0 )  , ( 10 , 0 )  ( - 10,0 )  , ( 10,0 )  ( − 10 , 0 )  , ( 10 , 0 )    asymptotes:   y = − 7 10 x , y = 7 10 x y = - \frac { 7 } { 10 } x , y = \frac { 7 } { 10 } x y = − 10 7 ​ x , y = 10 7 ​ x B) vertices:   ( − 10 , 0 )  , ( 10 , 0 )  ( - 10,0 )  , ( 10,0 )  ( − 10 , 0 )  , ( 10 , 0 )    asymptotes:   y = − 10 7 x , y = 10 7 x y = - \frac { 10 } { 7 } x , y = \frac { 10 } { 7 } x y = − 7 10 ​ x , y = 7 10 ​ x C) vertices:   ( 0 , − 7 )  , ( 0 , 7 )  ( 0 , - 7 )  , ( 0,7 )  ( 0 , − 7 )  , ( 0 , 7 )    asymptotes:   y = − 7 10 x , y = 7 10 x y = - \frac { 7 } { 10 } x , y = \frac { 7 } { 10 } x y = − 10 7 ​ x , y = 10 7 ​ x D) vertices:   ( 0 , − 10 )  , ( 0 , 10 )  ( 0 , - 10 )  , ( 0,10 )  ( 0 , − 10 )  , ( 0 , 10 )    asymptotes:   y = − 7 10 x , y = 7 10 x y = - \frac { 7 } { 10 } x , y = \frac { 7 } { 10 } x y = − 10 7 ​ x , y = 10 7 ​ x E) vertices:   ( − 7 , 0 )  , ( 7 , 0 )  ( - 7,0 )  , ( 7,0 )  ( − 7 , 0 )  , ( 7 , 0 )    asymptotes:   y = − 10 7 x , y = 10 7 x y = - \frac { 10 } { 7 } x , y = \frac { 10 } { 7 } x y = − 7 10 ​ x , y = 7 10 ​ x

Zybrea Knight · Accepted Answer

Final Answer : C, Explanation :   The given equation   y 2 49 − x 2 100 = 1 \frac { y ^ { 2 } } { 49 } - \frac { x ^ { 2 } } { 100 } = 1 49 y 2 ​ − 100 x 2 ​ = 1   represents a hyperbola with a vertical transverse axis. The vertices are found at   ( 0 , ± 49 ) (0, \pm \sqrt{49}) ( 0 , ± 49 ​ )  , which simplifies to   ( 0 , ± 7 ) (0, \pm 7) ( 0 , ± 7 )  . The asymptotes for a hyperbola of the form   y 2 a 2 − x 2 b 2 = 1 \frac { y ^ { 2 } } { a^2 } - \frac { x ^ { 2 } } { b^2 } = 1 a 2 y 2 ​ − b 2 x 2 ​ = 1   are given by   y = ± a b x y = \pm \frac { a } { b } x y = ± b a ​ x  , which in this case simplifies to   y = ± 7 10 x y = \pm \frac { 7 } { 10 } x y = ± 10 7 ​ x  .

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