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Math Help - Parabola Ellipse and Hyperbola

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    Parabola Ellipse and Hyperbola

    How will u classify the following curves in terms of parabola, ellipse or hyperbola?

    i) 17x^2+12xy+8y^2-46x-28y+33=0

    ii) x^2-5xy+y^2+8x-20y+15=0
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  2. #2
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    Quote Originally Posted by varunnayudu View Post
    How will u classify the following curves in terms of parabola, ellipse or hyperbola?

    i) 17x^2+12xy+8y^2-46x-28y+33=0

    ii) x^2-5xy+y^2+8x-20y+15=0
    Read this: Conic section - Wikipedia, the free encyclopedia
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  3. #3
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    Hello, varunnayudu!

    How will u classify the following curves as parabola, ellipse or hyperbola?

    1)\;\;17x^2+12xy+8y^2-46x-28y+33\:=\:0

    2)\;\;x^2-5xy+y^2+8x-20y+15\:=\:0
    If you are assigned "rotated" conics, you should have been given more information.

    We know the curve is rotated due to the appearance of the xy-term.


    The general quadratic has the form: . Ax^2 + Bxy + Cy^2 + Dx + Ey + F \;=\;0

    . . It has a "discriminant": . \Delta \:=\:B^2-4AC .
    ... look familiar?


    . . . . . . . . \begin{array}{|c|c|}\hline \Delta \:=\:0 & \text{parabola} \\ \hline \Delta \:<\:0 & \text{ellipse} \\ \hline \Delta \:>\:0 & \text{hyperbola}\\ \hline \end{array}

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  4. #4
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    can u give the answer

    i have solved the two eq and got an answer but need to see if its right or wrong ...........Can u give what type of conic do the two eq form
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  5. #5
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    Red face what do u think.

    Quote Originally Posted by Soroban View Post
    Hello, varunnayudu!

    If you are assigned "rotated" conics, you should have been given more information.

    We know the curve is rotated due to the appearance of the xy-term.


    The general quadratic has the form: . Ax^2 + Bxy + Cy^2 + Dx + Ey + F \;=\;0

    . . It has a "discriminant": . \Delta \:=\:B^2-4AC . ... look familiar?


    . . . . . . . . \begin{array}{|c|c|}\hline \Delta \:=\:0 & \text{parabola} \\ \hline \Delta \:<\:0 & \text{ellipse} \\ \hline \Delta \:>\:0 & \text{hyperbola}\\ \hline \end{array}

    I have done it this way .Is this right.........

    i) 17x^2 \ + \ 12xy \ + \ 8 y^2 \ - \ 46x \ - \ 28y \ + 33 \ = \ 0

     a \ = \ 17 ; \ b \ = \ 8 ; h \ = \ 6;

    ab-h^2 \ = \ 136 - 36 = \ 100

    since ab-h^2 > 0 therefore the eq is an hyperbola.

    ii)  x^2 - 5xy + y^2 + 8x - 20y +15 = 0

    a=1 ; \ b = 1; \ h = - \frac{5}{2}

    \therefore \ ab-h^2 = 1 - \frac{25}{4} = \frac{4 - 25}{4} = - \frac{21}{4} \ = -5.25 \ < \ 0

    \therefore since \ ab-h^2 < 0 it is an ellipse.
    Last edited by zorro; December 21st 2009 at 01:16 PM. Reason: rectified a mistake
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