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Question 674921: Use the center, vertices, and asymptotes to graph the hyperbola.
(x - 1)^2 - 9(y - 2)^2 = 9
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Use the center, vertices, and asymptotes to graph the hyperbola.
(x - 1)^2 - 9(y - 2)^2 = 9
(x-1)^2/9 -(y-2)^2 = 1
This is a hyperbola with horizontal transverse axis.
Its standard form of equation: , (h,k)=coordinates of center
For given hyperbola:
center: (1,2)
a^2=9
a=3
vertices: (1±a,2)=(1±3,2)=(-2,2) and (4,2)
b^2=1
b=1
asymptotes are straight lines that go thru center and take the form: y=mx+b, m=slope, b=y-intercept
slopes of asymptotes for hyperbolas with horizontal transverse axis=±b/a=±1/3
..
equation of asymptote with negative slope:
y=-x/3+b
solve for b using coordinates of center
2=-1/3+b
b=7/3
equation: y=-x/3+7/3
...
equation of asymptote with positive slope:
y=x/3+b
solve for b using coordinates of center
2=1/3+b
b=5/3
equation: y=x/3+5/3
see graph below:
y=±(((x-1)^2-9)/9)^.5+2
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