SOLUTION: Write the equation of a hyperbola with vertices at (1,1) and (9,1) and foci at (0,1)and (10,1).

Question 597704: Write the equation of a hyperbola with vertices at (1,1) and (9,1) and foci at (0,1)and (10,1).
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Write the equation of a hyperbola with vertices at (1,1) and (9,1) and foci at (0,1)and (10,1).
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Standard form of equation for a hyperbola with horizontal transverse axis:
(x-h)^2/a^2-(y-k)^2/b^2=1, (h,k)=(x,y) coordinates of center
For given hyperbola:
x-coordinate of center=(9+1)/2=5 (use midpoint formula)
y-coordinate of center=1
center: (5,1)
length of horizontal transverse axis=8 (from 1 to 9)=2a
a=4
a^2=16
..
Foci
2c=9 ( from 1 to 10)
c=4.5
..
c^2=a^2+b^2
b^2=c^2-a^2=20.25-16=4.25
..
Equation of hyperbola:
(x-5)^2/16-(y-1)^2/4.25=1

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