SOLUTION: Find the center, and the lengths of the transverse and conjugate axes of the hyperbola.Get the equation into standard form for a hyperbola. Find the center, and the lengths of the

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Question 876473: Find the center, and the lengths of the transverse and conjugate axes of the hyperbola.Get the equation into standard form for a hyperbola.
Find the center, and the lengths of the transverse and conjugate axes.
9x%5E2+-+16y%5E2+%2B+126x+%2B+288y+-+999+=+0
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Find the center, and the lengths of the transverse and conjugate axes.z
9x%5E2+-+16y%5E2+%2B+126x+%2B+288y+-+999+=+0
***
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
%28x%2B7%29%5E2%2F16-%28y-9%29%5E2%2F9=1
This is an equation of a hyperbola with horizontal transverse axis.
Its standard form of equation: %28x-y%29%5E2%2Fa%5E2-%28y-k%29%5E2%2Fb%5E2=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