math

sketch the conic r=2/1+cos theta

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  1. since e=1, it is a parabola, with vertex at (0,1) opening to the left.

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  2. Perhaps you feel more comfortable with rectangular graphing

    r=2/1+cos theta
    r = 2/(1+ x/r)
    r + x = 2
    √(x^2 + y^2) + x = 2
    √(x^2 + y^2) = 2-x
    square both sides
    x^2 + y^2 = 4 - 4x + x^2

    y^2 = 4 - 4x

    Steve meant to say, vertex is (1,0)

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  3. in (r,θ) it is (0,1)
    in (x,y) it is (1,0)

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  4. Dang - did I really say that?
    (1,0) in either case!

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