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.
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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: {{{(x-h)^2/a^2-(y-k)^2/b^2=1}}}, (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: {{{x^2/1156-y^2/61344=1}}}