<PRE><B>Question 686631</B>
I need to find the standard equation of a hyperbola with transverse axis at y=-5 with a length of 6 and conjugate axis at x=2 with a length of 6.
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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:
center: (2,-5)
given length of horizontal transverse axis=6=2a
a=3
a^2=9
given length of conjugate axis=6=2b
b=3
b^2=9
Equation of given hyperbola:
{{{(x-2)^2/9-(y+5)^2/9=1}}}
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