Question 746309: find an equations for the conic section that satisfies the given conditions. Hyperbola, foci (2,0), (2,8) asymptose y=3+1/2x y=5-1/2x
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! find an equations for the conic section that satisfies the given conditions. Hyperbola, foci (2,0), (2,8) asymptose y=3+1/2x y=5-1/2x
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Given hyperbola has a vertical transverse axis (y-coordinates of foci change but x-coordinates do not)
Its standard form of equation:  , (h,k)=(x,y) coordinates of center-
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center: (2,4)
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c=4 (distance from center to foci
c^2=16
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given slopes of asymptotes=±1/2=a/b (for hyperbolas with vertical transverse axis)
a/b=1/2
b=2a
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c^2=a^2+b^2
c^2=a^2+4a^2=5a^2
5a^2=16
a^2=16/5
a=4/√5
b^2=64√5
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Equation of given hyperbola:
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