Question 888569
Find an equation of a hyperbola having foci at (5-√13,-1) and (5+√13,-1) and asymptotes at y=2/3x-13/3 and y=-2/3x+7/3
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hyperbola has a horizontal transverse axis.
Its standard form of equation: {{{(x-h)^2/a^2-(y-k)^2/b^2=1}}}, (h,k)=coordinates of center
slopes of asymptotes=±2/3=b/a
b=±2a/3
b^2=4a^2/9
center: (5,-1)
c=√13
c^2=13=a^2+b^2
a^2+4a^2/9=13
9a^2+4a^2=117
13a^2=117
a^2=9
b^2=4a^2/9=36/9=4
equation: {{{(x-5)^2/9-(y+1)^2/4=1}}}