Question 616738: Find the standard form, graph, and find the asymptotes of the hyperbola
Verticies:(-10,3), (6,3). Focus: (-12,3), (8,3)
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Find the standard form, graph, and find the asymptotes of the hyperbola
Verticies:(-10,3), (6,3). Focus: (-12,3), (8,3)
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Given hyperbola has a horizontal transverse axis.
Its standard form of equation: (x-h)^2/a^2-(y-k)^2/b^2=1, (h,k)=(x,y) coordinates of center.
center: (-2,3)
length of horizontal transverse axis=16=2a
a=8
a^2=64
..
2c=20
c=10
c^2=100
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c^2=a^2+b^2
b^2=c^2-a^2=100-64=36
b=√36=6
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Equation of given hyperbola:
(x+2)^2/64-(y-3)^2/36=1
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slopes of asymptotes for hyperbolas with horizontal transverse axis=±b/a=±6/8=±3/4
asymptotes are straight lines that intersect at center: y=mx+b, m=slope, b=y-intercept
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Equation for asymptote with negative slope: y=-3x/4+b
solve for b using coordinates of center.
3=(-3*-2)/4+b
b=-3/2
equation: y=-3x/4+3/2
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Equation for asymptote with positive slope: y=3x/4+b
solve for b using coordinates of center.
3=(3*-2)/4+b
b=9
equation: y=3x/4+9/2
..
see graph below:
y=±((36(x+2)^2/64)-36)^.5+3
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