Question

Find parametric equations for the path of a particle that moves around the given circle in the manner described. x2 + (y - 3)2 = 4 (a) Once around clockwise, starting at (2, 3). X(t) = y(t) = Osts 211 (b) Three times around counterclockwise, starting at (2, 3). X(t) = 2cos(t) y(t) = Osts (c) Halfway around counterclockwise, starting at (0,5). x(t) = y(t) = Osts

Answer 1

parametric form of circle. x= r cosit) +h y = r sinct) +k here r= 2 h= K = 3 a) once round the clock weise, starting (213) Ost < 2 TT x= 2L05(-+) = 2 cos(+) t y= 2 sinct)+3 = 3- 2 sinct) / b) (213) Three times around wounterclockwise Period: Ost 5 OTT X= 2 cos(+) y= 2 sintt) +3 2 cos(t) 3+ 2 Gin(t)

c) Halfway around counter clock unise, starting at 10,5) B period: 0<t < TT we need to make x (t) and y(t) shifted too by 90° counter clockulise. allt)= 4los (t+1) -2 sin(t) y(t) = 2 sin( t+1D) +3 ) +3 = 3+ 2 cosct)