SOLUTION: Find the foci of the hyperbola. y^(2)-9x^(2)-4y-54x-86=0

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Question 633382: Find the foci of the hyperbola.
y^(2)-9x^(2)-4y-54x-86=0
Answer by lwsshak3(11628) About Me  (Show Source):
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Find the foci of the hyperbola.
y^(2)-9x^(2)-4y-54x-86=0
complete the square
y^2-4y-9x^2-54x-86=0
(y^2-4y+4)-9(x^2+6x+9)=86+4-81
(y-2)^2-9(x+3)^2=9
%28y-2%29%5E2%2F9-%28x%2B3%29%5E2%2F1=1
This is an equation of a hyperbola with vertical transverse axis.
Its standard form: %28y-k%29%5E2%2Fa%5E2-%28x-h%29%5E2%2Fb%5E2=1
For given equation:
center: (-3,2)
a^2=9
b^2=1
c^2=a^2+b^2=9+1=10
c=√10≈3.2
foci: (-3, 2±c)=(-3,2±3.2)=(-3+5.2) and (-3,-1.2)