Question 876473
Find the center, and the lengths of the transverse and conjugate axes.z
{{{9x^2 - 16y^2 + 126x + 288y - 999 = 0}}}
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9x^2+ 126x - 16y^2  + 288y - 999 = 0
complete the square:
9(x^2+ 14x +49) - 16(y^2 - 18y + 81) = 999+441-1296 
9(x+7)^2-16(y-9)^2=144
{{{(x+7)^2/16-(y-9)^2/9=1}}}
This is an equation of a hyperbola with horizontal transverse axis.
Its standard form of equation: {{{(x-y)^2/a^2-(y-k)^2/b^2=1}}}, (h,k)=coordinates of center
For given hyperbola:
center: (-7, 9)
a^2=16
a=4
length of transverse axis=2a=8
b^2=9
b=3
length of conjugate axis=2b=6