SOLUTION: I have a quiz tomorrow and I am having trouble solving the practice equation... Write 9x^2-108x+4y^2+8y+184=0 in standard form. Is it an ellipse, circle, parabola or hyperbola?

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: I have a quiz tomorrow and I am having trouble solving the practice equation... Write 9x^2-108x+4y^2+8y+184=0 in standard form. Is it an ellipse, circle, parabola or hyperbola?      Log On


   

Question 141450: I have a quiz tomorrow and I am having trouble solving the practice equation...
Write 9x^2-108x+4y^2+8y+184=0 in standard form. Is it an ellipse, circle, parabola or hyperbola?
Answer by nabla(475) About Me  (Show Source):
You can put this solution on YOUR website!
9x%5E2-108x%2B4y%5E2%2B8y%2B184=0
<--complete the squares
9%28x-6%29%5E2%2B4%28y%2B1%29%5E2%2B184-4-9%2A36=0<---factor
9%28x-6%29%5E2%2B4%28y%2B1%29%5E2=144<--simplify, shift constants to right-side
%28x-6%29%5E2%2B%284%2F9%29%28y%2B1%29%5E2=144%2F9<---divide 9 through to make x term standard
%281%2F4%29%28x-6%29%5E2%2B%281%2F9%29%28y%2B1%29%5E2=144%2F36<---divide 4 through to make the y term standard
%281%2F%2816%29%29%28x-6%29%5E2%2B%281%2F36%29%28y%2B1%29%5E2=1<---simplify it into standard form by dividing 4 through in order to make the right side 1.
%281%2F%284%29%5E2%29%28x-6%29%5E2%2B%281%2F%286%29%5E2%29%28y%2B1%29%5E2=1
It should be evident now that this is an ellipse, not a circle.
The center is (h,k) when in standard form: (6,-1).