SOLUTION: Find the foci for the following hyperbola 25x^2-9y^2+100x-54y+10=0

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Question 815010: Find the foci for the following hyperbola
25x^2-9y^2+100x-54y+10=0
Answer by lwsshak3(11628) About Me  (Show Source):
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Find the foci for the following hyperbola
25x^2-9y^2+100x-54y+10=0
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25x^2-9y^2+100x-54y+10=0
25x^2+100x-9y^2-54y=-10
complete the square:
25(x^2+4x+4)-9(y^2+6y+9)=-10+100-81
25(x+2)^2-9(y+3)^2=9
%28x%2B2%29%5E2%2F%289%2F25%29-%28y%2B3%29%5E2=1
This is a hyperbola with horizontal transverse axis.
Its standard form of equation: %28x-h%29%5E2%2Fa%5E2-%28y-k%29%5E2%2Fb%5E2=1, (h,k)=(x,y) coordinates of center.
For given hyperbola"
center:(-2,-3)
a^2=9/25
b^2=1
c^2=a^2+b^2=(9/25)+1=34/25
c=√34/5≈1.17
foci=(-2±c,-3)=(-2±1.17,-3)=(-3.17,-3) and (-.83,-3)