Answer
vertices: (-1,2±2)
foci: (-1,2±√13)
asymptotes: (y-2)=± $\frac{2}{3}$ (x+1)
Work Step by Step
9$y^{2}$-36y-4$x^{2}$-8x=4
9($y^{2}$-4y)-4($x^{2}$+2x)=4
9($(y-2)^{2}$-4)-4($(x+1)^{2}$-1)=4
After simplification:
9$(y-2)^{2}$-4$(x+1)^{2}$=36
$\frac{(y-2)^{2}}{4}$-$\frac{(x+1)^{2}}{9}$=1
From the equation of the hyberbola
the center = (-1,2)
$c^{2}$=$a^{2}$+$b^{2}$
$c^{2}$=4+9
c=√13
then the foci= (-1,2±√13)
vertices= (-1,2±2)
aymptotes= (y-2)=± $\frac{2}{3}$ (x+1)
