SOLUTION: Find the eccentricity of the curve 9x^2 - 4y^2 - 36x + 8y = 4 1) 1.80 2) 1.92 3) 1.82 4) 1.76

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Find the eccentricity of the curve 9x^2 - 4y^2 - 36x + 8y = 4 1) 1.80 2) 1.92 3) 1.82 4) 1.76      Log On


   

Question 520902: Find the eccentricity of the curve 9x^2 - 4y^2 - 36x + 8y = 4
1) 1.80
2) 1.92
3) 1.82
4) 1.76
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Find the eccentricity of the curve 9x^2 - 4y^2 - 36x + 8y = 4
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9x^2 - 4y^2 - 36x + 8y = 4
complete the square
9(x^2-4x+4)-4(y^2-2y+1)=4+36-4=36
9(x-2)^2-4(y-1)^2=36
divide by 36
9(x-2)^2/4-(y-1)^2/9=1
This is an equation of a hyperbola with horizontal transverse axis of the standard form:
(x-h)^2/a^2-(y-k)^2/b^2=1
For given equation:
a^2=4
a=√4=2
b^2=9
c^2=a^2+b^2=4+9=13
c=√13
Eccentricity,e=c/a=√13/2≈1.80