SOLUTION: I need to put this euqation into standard form. (Then find the center, vertices, foci, and asympotote- all those I know how to do. I just don't know how to put it in standard form,

Question 586649: I need to put this euqation into standard form. (Then find the center, vertices, foci, and asympotote- all those I know how to do. I just don't know how to put it in standard form, first!) Please help?!
Equation: 9x^2 - 4y^2 + 18x + 32y - 91 = 0
So far I wrote down:
(9x^2 + 18x) + (-4y^2 + 32y) = 91
1/2 (2) = 1^2 = 1
1/2 (8) = 4^2 = 16
9(x^2x+1)-4(y^2-8y+16) = 91 + 16 + 1
9(x^2x+1)-4(y^2-8y+16) = 108
And, I am stuck after that... help??

Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
I need to put this euqation into standard form. (Then find the center, vertices, foci, and asympotote- all those I know how to do. I just don't know how to put it in standard form, first!) Please help?!
Equation: 9x^2 - 4y^2 + 18x + 32y - 91 = 0
complete the squares
9(x^2+2x+1) - 4(y^2-8y+16)= 91+9-64
9(x+1)^2-4(y-4)^2=36
divide by 36
(x+1)^2/4-(y-4)^2/9=1
This is an equation of a hyperbola with horizontal transverse axis.
center: (-1,4)
a^2=4
b^2=9
I will let you do the rest as you said you knew how.
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