Question

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.

Answer 1

Answer:

  (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

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(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