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Math Help - finding values....

  1. #1
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    finding values....

    2x^2+Cy^2+Dx+Ey+F=0 represents a conic. state the values of C for which each of the following are possible

    a circle

    an ellipse

    a parabola

    a hyperbola
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  2. #2
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    The general form of a second-degree quadratic in 2 variables is
    Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0.

    We have to check the expression B^2 - 4AC to determine the type of conic.

    If B^2 - 4AC > 0, then we have a hyperbola.

    If B^2 - 4AC = 0, then we have a parabola.

    If B^2 - 4AC < 0, then we have either a circle or an ellipse. If B = 0 and A = C, then we have a circle. Otherwise, it's an ellipse.

    Now try your problem. B = 0 and A = 2...


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  3. #3
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    Hello, Dan!

    You're expected to know the general forms of the four conics.


    2x^2+Cy^2+Dx+Ey+F\:=\:0 represents a conic.
    State the values of C for which each of the following are possible:

    (a) a circle
    The coefficients of x^2 and y^2 must be equal.
    . . C \:=\:2



    (b) an ellipse
    The coefficients of x^2 and y^2 are unequal, but have the same sign.
    . . C \:>\:0\:\text{ and }\:C \:\neq\: 2



    (c) a parabola
    The equation has x^2 or y^2, but not both.
    . . C \:=\:0



    (d) a hyperbola
    The coefficients of x^2 and y^2 must have opposite signs.
    . . C \:<\:0

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