Question 669841: find the center,transverse axis, vertices, foci and asymptotes of the hyperbola;
4x^2-49y^2=196
Answer by MathLover1(20850)   (Show Source):
You can put this solution on YOUR website! given: 
First get it in standard form, which is either
 if the hyperbola opens right and left,
or
 if the hyperbola opens upward and downward.
note that:
the denominator of  term is greater than that of the  term, so the major axis is horizontal
Since  and  , then
 and 
so, the center is at ( ,  ) = ( , ).
 and  ,
the equation  gives you  ,
so 
and the eccentricity is 
the vertices and foci are above and below the center, so the foci are at
(, ) and (, ), which is
(, ) and (,  )
and the vertices are at (, ) and (, ) which is
(, ) and (, )
Because the  part of the equation is dominant , then the slope of the
asymptotes has the a on top, so the slopes will be  .
so, the asymptotes are  and 
graph:
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