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Math Help - Two Conic equations!

  1. #1
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    Two Conic equations!

    Well the teacher didn't get to this section and teaching myself did not work well lol.. I partly understand to an extent.

    The first example goes like
    Sketch the graph of the equation r = 3/(2-2sinθ)

    Now I doubt you'd be able to graph on this website, but I am wondering how to get to it.

    I know that, R= 3/(2-2sinθ) then R=3/2(1-sinθ) therefore R= (3/2) / 1-sinθ
    and since a=1, it is a parabola

    the next step goes like θ R but how do you work that into a graph?


    Second, would be ... Find an equation for the conic section r=1/(1+3sinθ) and i am less confident what to do on this part...
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  2. #2
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    Quote Originally Posted by aargh27 View Post
    Well the teacher didn't get to this section and teaching myself did not work well lol.. I partly understand to an extent.

    The first example goes like
    Sketch the graph of the equation r = 3/(2-2sinθ)
    r=3/(2-2sin θ)

    2r-2rsin θ=3
    2r-2y=3
    2r=3+2y
    (2r)^2=(3+2y)^2=9+12y+4y^2
    Thus,
    4x^2+4y^2=9+12y+4y^2
    4x^2-9=12y

    Is the conic (it is a parabola).
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  3. #3
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    I just worked out second problem.
    Is this right?

    r+3rsinθ=1
    r+3y=1
    r^2 +3y^2=1
    X^2 + y^2 +3y^2=1
    x^2 + 4y^2 =1
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  4. #4
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    Quote Originally Posted by aargh27 View Post
    I just worked out second problem.
    Is this right?

    r+3rsinθ=1
    r+3y=1
    r^2 +3y^2=1
    The mistake is here, not (a+b)^2 not = a^2+b^2
    (You need to multiply all possible products of the terms).

    r+3y=1
    r=1-3y
    r^2=(1-3y)^2
    x^2+y^2=1+6y+9y^2
    Now, combine and simplify.
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  5. #5
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    Hello, aargh27!

    Sketch the graph of the equation: .r .= .3/(2 - 2Ěsinθ)

    I know that: .r .= .3/(2 - 2Ěsinθ) .= .r .= .1.5/(1 - sinθ)
    and since a=1, it is a parabola. . Right!

    the next step goes like: .θ .R
    but how do you work that into a graph?

    We already know that it's a parabola.
    . . And it opens in one of four directions: left, right, up, or down.

    Plot points in the four compass-directions to get its orientation.

    θ = 0: . r .= .1.5/(1 - 0) .= .1.5

    θ = π/2: . r .= .1.5/(1 - 1) undefined . . . The parabola opens upward.

    θ = π: . r .= .1.5/(1 - 0) .= .1.5

    θ = 3π/2: . r .= .1.5/(1 - [-1]) .= .0.75


    This is enough to sketch the parabola.
    Code:
                          |
             *            |            *
                          |
              *           |           *
                          |
          - - - o - - - - + - - - - o - - -
               1.5        |        1.5
                    *     |     *
                         *o*
                          |0.75
                          |
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