SOLUTION: Write an equation of the hyperbola with vertices at (–7, 0) and (7, 0) and foci at (–9, 0) and (9, 0)

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Question 604372: Write an equation of the hyperbola with vertices at (–7, 0) and (7, 0) and foci at (–9, 0) and (9, 0)
Answer by lwsshak3(6463) About Me  (Show Source):
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Write an equation of the hyperbola with vertices at (–7, 0) and (7, 0) and foci at (–9, 0) and (9, 0)
This is a hyperbola with horizontal transverse axis.
Its standard form of equation: (x-h)^2/a^2-(y-k)^2/b^2=1, (h,k)=(x,y) coordinates of center.
For given hyperbola:
center: (0,0)
length of horizontal transverse axis=14=2a
a=7
a^2=49
..
foci
c=9
c^2=81
..
c^2=a^2+b^2
b^2=c^2-a^2=81-49=32
b=√32≈5.6
..
equation:
x^2/49-y^2/32=1