Which is the best co-ordinate scheme for parametric equations of lines and curves? Justify your answer...

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Which is the "best" co-ordinate scheme for parametric equations of lines and curves? Justify your answer in the context of the following questions: (a) Write down the parametric Cartesian co-ordinate equations for a cir- cle that lies in the XY plane (i.e. z=0) with radius 2, and centre at x=1, y=2. (b) Write down the parametric Cylindrical co-ordinate equations for a circle that lies in the XY plane (i.e. z=0) with radius 2, and centre at x=1, y=2. (c) Write down the parametric Spherical co-ordinate equations for a cir- cle that lies in the XY plane (i.e. z=0) with radius 2, and centre at x=0, y=0. Which is the "best" co-ordinate scheme for parametric equations of lines and curves? Justify your answer in the context of the following questions: (a) Write down the parametric Cartesian co-ordinate equations for a cir- cle that lies in the XY plane (i.e. z=0) with radius 2, and centre at x=1, y=2. (b) Write down the parametric Cylindrical co-ordinate equations for a circle that lies in the XY plane (i.e. z=0) with radius 2, and centre at x=1, y=2. (c) Write down the parametric Spherical co-ordinate equations for a cir- cle that lies in the XY plane (i.e. z=0) with radius 2, and centre at x=0, y=0.

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