Question 886273
What's the equation of the hyperbola with a focus at (-3-3*sqrt13,1), asymptotes intersecting at (-3,1) and one asymptote passing through the point (1,7)?
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center: (-3,1) (coordinates of asymptotes intersecting point)
Given hyperbola has a horizontal transverse axis.(center and focus have the same y-coordinate(1)
Standard form of equation for a hyperbola with horizontal transverse axis: 
{{{(x-h)^2/a^2-(y-k)^2/b^2=1}}}, (h,k)=coordinates of center
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asymptotes are straight lines that take the form: y=mx+b, m=slope, b=y-intercept
For given hyperbola:
Using given points, (-3,1) and (1,7) on one of the asymptotes:
slope=∆y/∆x=(7-1)/(1-(-3))=6/4=3/2
slope of other asymptote=-3/2
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slope = b/a=3/2
b=3a/2
c^2=a^2+b^2
c^2=a^2+9a^2/4
c^2=13a^2/4
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focus=(-3-3√13,1)
c=-3-3√13+3≈10.82
c^2=117
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117=13a^2/4
13a^2=4*117=468
a^2=468/13=36
b^2=9a^2/4=81
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Equation of given hyperbola: 
{{{(x+3)^2/36-(y-1)^2/81=1}}}