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

Dale Tate

Dale Tate

Answered question

2022-06-11

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)?

Answer & Explanation

Amy Daniels

Amy Daniels

Beginner2022-06-12Added 20 answers

Step 1
It 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>0)
Step 2
If x = 2 cos ( t ) and y = 2 - 2 sin ( t ) for t 0 the point starts moving from (2,2) clockwise

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