Question 1186254
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Vertices: (15, 1), (-1, 1); Endpoints of Conjugate Axis: (7, 7), (7, -5).


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Since the conjugate axis is mentioned, it is about hyperbola.


Its center is the point  (7,1).


It has horizontal major axis y = 1, parallel to x-axis.

The distance between vertices is  15 - (-1) = 16;  hence, the major semi-axis length  "a"  is  16/2 = 8  units.


It has vertical conjugate axis  x = 7, parallel to y-axis.

The length of the conjugate axis is 7 - (-5) = 12;  hence, the minor semi-axis length  "b"  is  12/2 = 6  units.



Combining all this info, the standard equation of the hyperbola is


    {{{(x-7)^2/8^2}}} - {{{(y-1)^2/6^2}}} = 1.
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Solved.