Question 464909: Write an equation for the hyperbola with vertices (0,4) and (0,-4) if the length of the conjugate axis is 6 units. Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website! Write an equation for the hyperbola with vertices (0,4) and (0,-4) if the length of the conjugate axis is 6 units.
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Given data shows this is a hyperbola with center of at (0,0), and a vertical transverse axis.
length of transverse axis=8=2a
a=4
a^2=16
Length of conjugate axis =6=2b
b=3
b^2=9
Standard form of hyperbola with vertical transverse axis: (y-k)^2/a^2+(x-h)^2/9=1
For given problem:
Equation: y^2/16-x^2/9=1
see graph below as a visual check
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y=(16+16x^2/9)^.5
±4x/3
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