SOLUTION: 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

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-
..
center: (2,4)
..
c=4 (distance from center to foci
c^2=16
..
given slopes of asymptotes=�1/2=a/b (for hyperbolas with vertical transverse axis)
a/b=1/2
b=2a
..
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
..
Equation of given hyperbola:

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