SOLUTION: find the center,transverse axis, vertices, foci and asymptotes of the hyperbola; 4x^2-49y^2=196

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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