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Question 689066: Can someone please help me find the foci and asymptotes to (y-1)^2/9-(x-3)^2/4=1
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! find the foci and asymptotes to
(y-1)^2/9-(x-3)^2/4=1
This is an equation of a hyperbola with vertical transverse axis (y-term listed first)
Its standard form of equation:  , (h,k)=(x,y) coordinates of center
For given equation: 
center: (3,1)
a^2=9
a=√9=3
b^2=4
b=√4=2
c^2=a^2+b^2=9+4=13
c=√13≈3.6
foci: (3,1±c)=(3,1±3.6)=(3,-2.6) and (3,4.6)
Asymptotes: Straight line equations that go thru center, y=mx+b, m=slope, b=y-intercept
slopes of asymptotes for hyperbolas with vertical transverse axis=±a/b=±3/2
equation of asymptote with negative slope:
y=-3x/2+b
solve for b using coordinates of center(3,1)
1=-3*3/2+b
b=1+9/2=11/2
equation of asymptote:
y=-3x/2+11/2
..
equation of asymptote with positive slope:
y=3x/2+b
solve for b using coordinates of center(3,1)
1=3*3/2+b
b=1-9/2=-7/2
equation of asymptote:
y=3x/2-7/2
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