SOLUTION: WHY can you use the discriminant, {{{ b^2-4ac )}} to determine whether the second degree equation {{{ Ax^2+Bxy+Cy^2+Dx+Ey+F=0 }}} graphs as a hyperbola (if the discriminant is gr

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: WHY can you use the discriminant, {{{ b^2-4ac )}} to determine whether the second degree equation {{{ Ax^2+Bxy+Cy^2+Dx+Ey+F=0 }}} graphs as a hyperbola (if the discriminant is gr      Log On


   

Question 290767: WHY can you use the discriminant, graphs as a hyperbola
(if the discriminant is greater than 0), parabola (if the discriminant is equal to 0), and an ellipse (if the discriminant is less than zero)?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
WHY can you use the discriminant, b^2-4ac graphs as a hyperbola
(if the discriminant is greater than 0), parabola (if the discriminant is equal to 0), and an ellipse (if the discriminant is less than zero)?
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b^2-4ac is used to determine whether a quadratic
has 2 Real and unequal, 2 Real but equal, or
2 Complex soltuions. It does not tell you whether
you have a hyperbola, parabola, or ellipse.
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Cheers,
Stan H.