SOLUTION: Find the coordinate of the vertices and foci and the equation of the asymptotes for the hyperbola with the equation (y^2/16)-(x^2/25)=1

Algebra ->  Finance -> SOLUTION: Find the coordinate of the vertices and foci and the equation of the asymptotes for the hyperbola with the equation (y^2/16)-(x^2/25)=1      Log On


   

Question 1142077: Find the coordinate of the vertices and foci and
the equation of the asymptotes for the hyperbola
with the equation (y^2/16)-(x^2/25)=1
Answer by ikleyn(52775) About Me  (Show Source):
You can put this solution on YOUR website!
.

            I will show you how to find the equations for the hyperbola's asymptotes. 


The hyperbola is given by equation


    y%5E2%2F16 - x%5E2%2F25 = 1.     (1)


The equation for the asymptotes is


    y%5E2%2F16 - x%5E2%2F25 = 0.      (2)


It is obtained from the standard equation of the hyperbola (1) replacing "1" in the right side of the hyperbola' standard equation by "0".


The equation (2) deploys in two equations (3) and (4) below for the two straight asymptotes in this way


    %28y%2F4+%2B+x%2F5%29%2A%28y%2F4+-+x%2F5%29 = 0  =================>


    y%2F4+%2B+x%2F5 = 0    (3),   and

    y%2F4+-+x%2F5 = 0.   (4)


You can further transform these equations for asymptotes (3), (4) to any other appropriate equivalent form.

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For similar problem, see my post at the link

    https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1142075.html

in the archive of this forum.