Question 692052
Draw the hyperbolas and the eccentricity of the following: 
4x^2 - 9y^2 - 16x + 18y = 29
complete the square
4x^2-16x-9y^2+18y=29
4(x^2-4x+4)-9(y^2-2y+1)=29+16-9
4(x-2)^2-9(y-1)^2=36
{{{(x-2)^2/9-(y-1)^2/4=1}}}
This is an equation of a hyperbola with horizontal transverse axis.
Its standard form of equation: {{{(x-h)^2/a^2-(y-k)^2/b^2=1}}}, (h,k)=(x,y) coordinates of center
For given equation:{{{(x-2)^2/9-(y-1)^2/4=1}}}
center: (2,1)
a^2=9
a=√9=3
b^2=4
b=√4=2
c^2=a^2+b^2=9+4=13
c=√13
eccentricity=c/a=√13/3 (there is no graph for this)
see graph below
y=±(4(x-2)^2/9-4)^.5+1
{{{ graph( 300, 300, -10, 10, -10, 10,(4(x-2)^2/9-4)^.5+1,-(4(x-2)^2/9-4)^.5+1) }}}