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Math Help - hi! conics

  1. #1
    bay
    bay is offline
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    Question hi! conics

    I am need of help!
    the equation 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
    b) ellipse
    c) parabola
    d) hyperbola

    so I am not sure but here is my guess:
    a) circle: c=90
    b) ellipse: c=50
    c) parabola c=?
    d) hyperbola c=?

    I am not even sure?
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  2. #2
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    Quote Originally Posted by bay View Post
    I am need of help!
    the equation 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
    b) ellipse
    c) parabola
    d) hyperbola
    You need to look at the discrimanat.
    The xy term is zero here.
    And the x^2 term is 2 and y^2 term is c.
    Thus,
    -4(2)(c)^2=-8c^2
    Thus,
    -8c^2>0 if c\not = 0 and we have an ellipse of a circle.
    And only when c=0 we have -8c^2=0 thus we have parabola.
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  3. #3
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    Hello, bay!

    Evidently, you need help . . .


    The equation 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 . . b) ellipse . . c) parabola . . d) hyperbola

    a) Circle
    The coefficients of x^2 and y^2 must be equal.
    . . Hence: . c = 2

    b) Ellipse
    The coefficients of x^2 and y^2 must have the same sign but unequal.
    . . Hence: . c > 0,\;c \neq 2 . (any positive number except 2)

    c) Parabola
    Either the coefficient of x^2 or the coefficient of y^2 must be zero.
    . . Hence: .  c = 0

    d) Hyperbola
    The coefficients of x^2 and y^2 must have oppsite signs.
    . . Hence: . c < 0 . (any negative number)

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