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Question 553468: what are the equations for both asymptotes of the following hyperbola (y^2)/(16)-(x^2)/(9)=1
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! what are the equations for both asymptotes of the following hyperbola (y^2)/(16)-(x^2)/(9)=1
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(y^2)/(16)-(x^2)/(9)=1
This is an equation of a hyperbola with vertical transverse axis.
Its standard form: (x-h)^2/a^2-(y-k)^2/b^2=1, with (h,k) being the (x,y) coordinates of the center.
For given equation:
Center: (0,0)
a^2=16
a=√16=4
b^2=9
b=√9=3
Asymptotes for hyperbolas are straight lines which go thru the center and are of the standard form: y=mx+b, m=slope, b=y-intercept.
For given equation:
Slopes of asymptotes: ±a/b=±4/3
y-intercept=0
Equation of asymptotes:
y=-4x/3+0=-4x/3
and
y=4x/3+0=4x/3
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