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Math Help - Name the Curve

  1. #1
    Len
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    Name the Curve

    Name the curve with the given polar equation

    1) r=4
    r^2=4^2

    x^2+y^2=4^2

    Circle with radius 4 and origin (0,0)

    2) \Theta=\dfrac{2\Pi}{3}
    Stumped.

    3) r=-4\cos\Theta

    \cos\Theta=\dfrac{x}{r}

    => r=-4\dfrac{x}{r}

    => r^2=-4x

    x^2+4x+y^2=0

    (x+2)^2+y^2=2^2

    Circle with radius 2 and origin (-2,0)

    If someone could verify 1 & 3 and help with the 2 I would be most appreciative. Thanks.
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  2. #2
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    Quote Originally Posted by Len View Post
    Name the curve with the given polar equation

    1) r=4
    r^2=4^2<br /> <br />
x^2+y^2=4^2

    Circle with radius 4 and origin (0,0)

    2) \Theta=\dfrac{2\Pi}{3}
    Stumped.

    3) r=-4\cos\Theta

    \cos\Theta=\dfrac{x}{r}

    => r=-4\dfrac{x}{r}

    => r^2=-4x

    x^2+4x+y^2=0

    (x+2)^2+y^2=2^2

    Circle with radius 2 and origin (-2,0)

    If someone could verify 1 & 3 and help with the 2 I would be most appreciative. Thanks.
    1) Correct
    2) Only an angle is specified. Hence r can be anything. Hence it is just an infinite straight line at that angle from the positive x axis.
    3) Correct.
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