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21 July, 00:11

For each of the described curves, decide if the curve would be more easily given by a polar equation or a Cartesian equation. Then write an equation for the curve. (a) A circle with radius 4 and center (2, 2). (b) A circle centered at the origin with radius 2.

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  1. 21 July, 00:59
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    (a) (x-2) ^2 + (y-2) ^2 = 16

    (b) r = 2

    Step-by-step explanation:

    (a) When the circle is offset from the origin, the equation for the radius gets messy. In general, it will be the root of a quadratic equation in sine and cosine, not easily simplified. The Cartesian equation is easier to write.

    Circle centered at (h, k) with radius r:

    (x - h) ^2 + (y - k) ^2 = r^2

    The given circle is ...

    (x - 2) ^2 + (y - 2) ^2 = 16

    __

    (b) When the circle is centered at the origin, the radius is a constant. The desired circle is most easily written in polar coordinates:

    r = 2
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