SOLUTION: Could you kindly help with the following problem Draw the hyperbolas and the eccentricity of the following: 4x^2 - 9y^2 - 16x + 18y = 29 I having a hard time getting into

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Could you kindly help with the following problem Draw the hyperbolas and the eccentricity of the following: 4x^2 - 9y^2 - 16x + 18y = 29 I having a hard time getting into       Log On


   

Question 692052: Could you kindly help with the following problem
Draw the hyperbolas and the eccentricity of the following:
4x^2 - 9y^2 - 16x + 18y = 29
I having a hard time getting into the hyperbola standard equation


Regards,
Gheomell
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
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
%28x-2%29%5E2%2F9-%28y-1%29%5E2%2F4=1
This is an equation of 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 equation:%28x-2%29%5E2%2F9-%28y-1%29%5E2%2F4=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