I have the hyperbola from a textbook 9x^2 - 18x - 16y^2 - 64y = 91
It is supposed to become: ((x-1)^2) / 4 - ((y+2)^2) / (9/4) = 1
I cannot get this though, I arrive at: ((x-1)^2) / 4 - ((y+2)^2) / (9/-4) = 1
what I am doing is
that -4 doesn't work... What am i doing wrong? I figure i can't leave a -y^2 since it would mess things up? So i factor out -16 to begone of the negative but I am left with a negative later in the denominator, which doesn't really work with roots. What am I missing?
Hint
Rewrite, just as you properly did at the beginning of your work, $$9x^2 - 18x - 16y^2 - 64y = 91$$ $$9(x^2 - 2x) - 16(y^2 + 4y) = 91$$ $$9(x^2 - 2x + 1 -1) - 16(y^2 + 4y+4 -4) = 91$$ $$9((x-1)^2 -1) - 16((y+2)^2 -4) = 91$$ $$9(x-1)^2 -9 - 16(y+2)^2+64 = 91$$ $$9(x-1)^2 - 16(y+2)^2 = 91+9-64=36$$ Now notice that $\frac{9}{36}=\frac{1}{4}$ and that $\frac{16}{36}=\frac{4}{9}$.
I am sure that you can take from here.