Discriminants for ellipse, parabola or hyperbola

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The discussion focuses on using the discriminant to classify conic sections from given equations. The user presents five equations and shares their classifications based on calculated discriminant values. The results include two parabolas, two hyperbolas, and one ellipse. A question arises regarding the classification of the third equation, suggesting it should be a hyperbola instead of a parabola. The conversation emphasizes the importance of accurate discriminant calculations for proper classification of conic sections.
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Homework Statement



Use the discriminant to determine if the following are equations of an ellipse, parabola or hyperbola

6x^2-12xy+6y^2-5x+9=0
5xy-4y^2+8x-3y+20=0
x^2-9xy+5y^2-2=0
10x^2-9xy+5y^2-2=0
2y^2-10x+9y-8=0

Homework Equations



The Attempt at a Solution



I got these answers:

0, parabola
25, hyperbola
44, hyperbola
-119, ellipse
0, parabola

could someone check me on these? Thanks!
 
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Shouldn't the third one be 81-4*1*5=61,hyperbola? Was that so hard you really needed a check?
 

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