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Question 593433: Find the equation for a hyperbola with vertices (4,0) and (-4,0) and asymptote y=1/2x.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Find the equation for a hyperbola with vertices (4,0) and (-4,0) and asymptote y=1/2x.
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Standard form of an equation for a hyperbola with horizontal transverse axis:
(x-h)^2/a^2-(y-k)^2/b^2=1
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For given hyperbola:
y-coordinate of center=0
x-coordinate of center=0 (midway between 4 and -4)
center: (0,0)
length of horizontal transverse axis=8 (-4 to 4)=2a
a=4
a^2=16
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Slope of asymptote=b/a=1/2
b=a/2=4/2=2
b^2=4
Equation:
x^2/16-y^2/4=1
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