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Thread: hi! conics

  1. #1
    bay
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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 $\displaystyle xy$ term is zero here.
    And the $\displaystyle x^2$ term is 2 and $\displaystyle y^2$ term is c.
    Thus,
    $\displaystyle -4(2)(c)^2=-8c^2$
    Thus,
    $\displaystyle -8c^2>0$ if $\displaystyle c\not = 0$ and we have an ellipse of a circle.
    And only when $\displaystyle c=0$ we have $\displaystyle -8c^2=0$ thus we have parabola.
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  3. #3
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    Hello, bay!

    Evidently, you need help . . .


    The equation $\displaystyle 2x^2+cy^2+dx+ey+f\:=\:0$ represents a conic.
    State the values of $\displaystyle c$ for which each of the following are possible.

    a) circle . . b) ellipse . . c) parabola . . d) hyperbola

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

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

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

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

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