Question 737278: Find an equation of the hyperbola with foci at (0, 0) and (250, 0), whose points are all 68 units closer to one focus than the other.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Find an equation of the hyperbola with foci at (0, 0) and (250, 0), whose points are all 68 units closer to one focus than the other.
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Given data shows hyperbola has a horizontal transverse axis. (x-coordinates of foci change, but y-coordinates do not)
Its standard form of equation:  , (h,k)=(x,y) coordinates of center.
By definition: The difference in distances between a point on the hyperbola and each of the foci=68=2a
a=34
a^2=1156
c=250 (distance from center (0,0),to focus (250,0)
c^2=62500
c^2=a^2+b^2
b^2=c^2-a^2=62500-1156=61344
Equation: 
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