SOLUTION: find the standard form of the equation of the hyperbola given the Vertices: (2,0), (6,0); Foci: (0,0), (8,0)

Question 722933: find the standard form of the equation of the hyperbola given the Vertices: (2,0), (6,0); Foci: (0,0), (8,0)
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
find the standard form of the equation of the hyperbola given the Vertices: (2,0), (6,0); Foci: (0,0), (8,0)
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given data shows that hyperbola has a horizontal transverse axis: (x-coordinates change but y-coordinates do not)
standard form of equation of given hyperbola: , (h.k)=(x,y) coordinates of the center
x-coordinate of center=4(midpoint of vertices and foci)
y-cooordinate of center=0
center: (4,0)
length of horizontal transverse axis=4 (2 to 6)=2a
a=2
a^2=4
distance between foci=8=2c
c=4
c^2=16
c^2=a^2+b^2
b^2=c^2-a^2=16-4=12
equation of given hyperbola:
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