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Use vertices and asymptotes to graph each hyperbola. Locate the foci and find the equations of the asymptotes. y^/25-x^/64=1
This is an equation of a hyperbola with vertical transverse axis of the standard form:
For given equation:
Length of vertical transverse axis=2a=10
Vertices (end points of transverse axis): (0,0±a)=(0,0±5)=(0,5) and (0-5)
Foci: (0,0±c)=(0,±√89)=(0,√89) and (0,-√89)
Equation of asymptotes which are straight lines of the standard form: y=mx+b, m=slope,
b=y-intercept. Asymptotes also go thru center at (0,0) in this case, so y-intercept=0.
Equation of asymptotes: y=±5x/8
See graph below as a visual check on answers: