How to find the center, vertices, foci and eccentricity of x 2 36 + y 2 64 = 1 ?

Question

How to find the center, vertices, foci and eccentricity of                     x        2            36        +                  y        2            64        =    1  ?

Gerald Dickerson · Accepted Answer

x        2            36        +                  y        2            64        =    1  Compared to the standard ellipse equation                     x        2                    a        2              +                  y        2                    b        2              =    1  ,             a      2        =    36    ,          b      2        =    64    ⇒    b    =    8    &amp;gt;    6    =    a  Therefore, the eqn. represents an Ellipse with Major axis along Y- axis &amp;amp; Minor Axis along X-axisThe Eccentricity e is given by,             a      2        =          b      2              (      1      -              e        2            )        ⇒    36    =    64          (      1      -              e        2            )        ⇒          36      64        =    1    -          e      2            ∴          e      2        =    1    -          36      64        =    1    -          9      16        =          7      16        ⇒    e    =                  7            4      The Focii are       S          (      0      ,      b      e      )        =    S          (      0      ,      8      ⋅                        7                4            )        =    S          (      0      ,      2              7            )       &amp;amp;       S    ′          (      0      ,      -      b      e      )        =    S    ′          (      0      ,      -      2              7            )       The Centre of the ellipse is       C          (      0      ,      0      )      .The Vertices are       A          (      a      ,      0      )        =    A          (      6      ,      0      )        ,    A    ′          (      -      a      ,      0      )        =    A    ′          (      -      6      ,      0      )        ,    B          (      0      ,      b      )        =    B          (      0      ,      8      )        ,    B    ′          (      0      ,      -      b      )        =    B    ′          (      0      ,      -      8      )

How to find the center, vertices, foci and eccentricity of x^2/36+y^2/64=1?

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