Question 738568
Find the equation for the hyperbola centered at the origin and satisfies these conditions.
The foci are the points (+-8,0) and the length of the transverse axis is 2.
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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:
given center:(0,0)
given length of horizontal transverse axis=2=2a
a=1
a^2=1
c=8 (distance from center to foci)
c^2=64
c^2=a^2+b^2
b^2=c^2-a^2=64-1=63
equation for the hyperbola:
{{{x^2/1-y^2/63=1}}}