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Question 459116: how do I graph 25(x+2)^2-9(y-1)^2=225
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! how do I graph 25(x+2)^2-9(y-1)^2=225
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25(x+2)^2-9(y-1)^2=225
divide by 225
(x+2)^2/9-(y-1)^2/25=1
This equation is a hyperbola with horizontal transverse axis. (Note the minus sign and the x-term comes before the y-term)
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Standard form of a hyperbola with horizontal transverse axis: (x-h)^2/a^2-(y-k)^2/b^2=1, with (h,k) being the (x,y) coordinates of the center.
Standard form of a hyperbola with vertical transverse axis: (y-k)^2/a^2-(x-h)^2/b^2=1, with (h,k) being the (x,y) coordinates of the center.
The difference between the two forms is the interchange of (x-h) and (y-k)
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center(-2,1)
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a^2=9
a=3
length of transverse axis=2a=6
vertices=(-2±3,1)=(-5,1) and (1,1)
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b^2=25
b=5
length of conjugate axis=2b=10
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Asymptotes:
slope, m=±b/a=±5/3
Equations:
y=mx+b
1=5(-2)/3+b
b=1+10/3=13/3
y=5x/3+13/3
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1=-5(-2)/3+b
b=1-10/3=-7/3
y=-5x/3-7/3
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y=(-25+25(x+2)^2/9)^.5+1
See graph below as a visual check on answers above:
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