Question 698269: write the equation of the hyperbola with vertices (6,0) and (-6,0) and an asymptote of y=1/2x
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! write the equation of the hyperbola with vertices (6,0) and (-6,0) and an asymptote of y=1/2x
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This is a hyperbola with 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
..
For given hyperbola:
center: (0,0)
length of horizontal transverse axis=12=2a (-6 to 6)
a=6
a^2=36
For hyperbolas with horizontal transverse axis, slope of asymptotes=b/a
b/a=1/2
b=a/2
b=6/2=3
b^2=9
Equation:
x^2/36-y^2/9=1
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