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)?

1 Answer
Salvatore I.
Nov 2, 2016

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

Explanation:

It is enough to pose #x=2cos(t)# and #y-2=2sin(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=2-2sin(t)# (for t>0)

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