How to identify the vertices, foci, and direction of y 2 25 - x 2 16 = 1 ?

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How to identify the vertices, foci, and direction of                     y        2            25        -                  x        2            16        =    1  ?

Keegan Herman · Accepted Answer

The equation is                    y        2            25        -                  x        2            16        =    1        ⇒  This represents a hyperbola&#039;s vertical transverse axis equation.                    y        2                    a        2              -                  x        2                    b        2              =    1  The center of the hyperbola is       C    =          (      0      ,      0      )      The vertices are       V    =          (      0      ,      5      )       and       V    ′    =          (      0      ,      -      5      )      The foci are       F    =          (      0      ,      c      )       and       F    ′    =          (      0      ,      -      c      )      where       c    =                            a          2                +                  b          2                      =                  25        +        16              =          41      The foci are       F    =          (      0      ,              41            )       and       F    ′    =          (      0      ,      -              41            )      The asymptotes are       y    =    ±          (              a        b            )        x  The asymptotes are       y    =    ±          (              5        4            )        x  graph{y^2/25-x^2/16=1 [-32.47, 32.47, -16.25, 16.24]}

How to identify the vertices, foci, and direction of y^2/25-x^2/16=1?

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