SOLUTION: how do i find the asymptotes for (y^2/16)-(x^2/81)=1

Question 820619: how do i find the asymptotes for (y^2/16)-(x^2/81)=1
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
how do i find the asymptotes for
(y^2/16)-(x^2/81)=1
This is an equation of a hyperbola with vertical transverse axis.
Its standard form of equation: , (h,k)=(x,y) coordinates of center.
..
Asymptotes of hyperbolas are straight-line equations that go through the center.
Their standard form: y=mx+b, m=slope, b=y-intercept
slopes of hyperbolas with vertical transverse axis=�a/b
slopes of hyperbolas with horizontal transverse axis=�b/a
..
For given hyperbola:
center: (0,0)
a^2=16
a=√16=4
b^2=81
b=√81=9
slopes of asymptotes=�a/b=�4/9
..
Equation of asymptote with positive slope:
y=(4/9)x+b
solve for b using coordinates of center:
b=y-intercept=0
equation: y=4x/9
..
Equation of asymptote with negative slope:
y=(-4/9)x+b
b=0
equation:y=-4x/9
RELATED QUESTIONS
Find the equations of the asymptotes.... (answered by richwmiller)

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

How do you find asymptotes? For example,... (answered by MathLover1)

how do you find the vertices, co-vertices, foci, and asymptotes of: 9(x+2)^2... (answered by lwsshak3)

How do I find all the asymptotes of... (answered by stanbon,Nate)

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

How do i find the Center, Vertices, Foci and the Equation of the asymptotes of the... (answered by lwsshak3)

Find the center, vertices, foci, and asymptotes of the hyperbola. {{{(x+4)^2/16 -... (answered by lwsshak3)

Find the asymptotes for... (answered by jim_thompson5910)