How do you find parametric equations for the path of a particle that moves around the given circle x 2 + ( y – 2 ) 2 = 4 clockwise, starting at (2, 2)?

Question

How do you find parametric equations for the path of a particle that moves around the given circle             x      2        +                  (        y        –        2        )            2        =    4   clockwise, starting at (2, 2)?

Amy Daniels · Accepted Answer

Step 1It is enough to pose       x    =    2          cos              (        t        )             and       y    -    2    =    2          sin              (        t        )             and then to replace them into equation of the circumference to find an identity!As we want to move closkwise we can choose values of the parameter t that are negativa or use positive values provided that we make a parameter change from t to -t so that the parametrical equations for x reamains unchanged whereas the one for y gets       y    =    2    -    2          sin              (        t        )             (for t&amp;gt;0)Step 2If       x    =    2          cos              (        t        )             and       y    =    2    -    2          sin              (        t        )             for       t    ≥    0   the point starts moving from (2,2) clockwise

How do you find parametric equations for the path of a particle that moves around the given circle

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