Question 1168977
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Conjugate axis along the y-axis, one vertex at (0,7), asymptotes are 6x-5y+30=0 and 6x+5y-30=0. 
Need help finding the Equation of this hyperbola. How?
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            Regarding this post,  I have two notices.



First notice is that the problem's formulation is  INCORRECT  and  SELF-CONTRADICTORY.
It describes a situation which  NEVER  may happen in reality.


Indeed,  the problem says that conjugate axis of the hyperbola is along  y-axis,
one vertex is  (0,7)  and the asymptotes are  6x-5y+30 = 0  and  6x+5y-30 = 0.


From equations,  the center of the hyperbola is  (x,y) = (0,6).


Together with the information about  " one vertex ",  it means that transverse axis is vertical y-axis, 
and it contradicts that the conjugate axis is  y-axis,  as stated in the post.



            It disproves the problem,  kills it to the death and ruins it into dust.



Second notice is that the solution in the post by @CPhill is  TOTALLY  and  FATALLY  incorrect,
starting from his first two lines,  where he writes an equation of the hyperbola in  WRONG  FORM.


So,  the problem itself is  {{{highlight(highlight(IDIOTIC))}}},  as well as its  " solution "  produced and presented by @CPhill.


For the peace in your mind,  my dear reader,  ignore both the problem and its  " solution "  by @CPhill.



            A right place for such compositions is a trash bin.