SOLUTION: Find the coordinate of the vertices and foci and the equation of the asymptotes for the hyperbola with the equation (y-3)^2/25-(x-2)^2/16=1

Question 1142078: Find the coordinate of the vertices and foci and
the equation of the asymptotes for the hyperbola
with the equation (y-3)^2/25-(x-2)^2/16=1
Answer by ikleyn(52781) (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


     -  = 1.     (1)


The equation for the asymptotes is


     -  = 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


     = 0  =================>


     = 0    (3),   and

     = 0.   (4)


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

-------------

For similar solved problems, see my posts at the links

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

https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1142077.html

in the archive of this forum.

RELATED QUESTIONS
Find the coordinate of the vertices and foci and the equation of the asymptotes for the... (answered by greenestamps,ikleyn)

Find the coordinate of the vertices and foci and the equation of the asymptotes for the... (answered by ikleyn)

Find the coordinate of the vertices and foci and the equation of the asymptotes for the... (answered by Edwin McCravy)

Find the coordinate of the vertices and foci and the equation of the asymptotes for the... (answered by greenestamps)

Find the coordinates of the vertices and foci and the equations of the asymptotes for the (answered by lwsshak3)

find the vertices,foci and equation of asymptotes of x^2-2y^2=2 for the... (answered by lwsshak3)

Given the hyperbola with the equation y^2 -9x^2 =-9 find the vertices, the foci, and... (answered by Edwin McCravy)

Find the coordinate of the vertices and foci and the equation of the asymptotes for the... (answered by Edwin McCravy,ikleyn)

Find the coordinates of the vertices and foci and the equations of the asymptotes for the (answered by ewatrrr)