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

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) (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

This is an equation of a hyperbola with horizontal transverse axis.
Its standard form of equation: , (h,k)=(x,y) coordinates of center
For given equation:
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

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