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

Question 633382: Find the foci of the hyperbola.
y^(2)-9x^(2)-4y-54x-86=0
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
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

This is an equation of a hyperbola with vertical transverse axis.
Its standard form:
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)

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