Question

1. Find parametric equations and a parameter interval for the motion of the particle starting at the point (2,0) and tracing the top half of the circle x2 + y2 - 4 four times =1 2.Replace the cartesian equation with polar equation x2y 9 xy = 2 (x - 3)" + (y + 1)? - 4 3. Identify the symmetries of the curves. Then sketch the curves in the x-y plane a) = 2-2cost b)r? - sint 1. Give a geometric description of the set of points in space whose coordinates satisfy the given parts of the equation A) x2 + y2 + 2? - 25 wY-4 b) zy? X=1

Answer 1

ANDA Saution! Equation of circle is and y = 2 sint xay y let da zoost x?ty - (2cost) + Casint) 22 We are 4 cost & usine sin't + wst al "(cost + Sin²t) = 4 Hervey = 2sint is always positive Juice fracing the top half of the circle ThereforeIlu Parametri equalions are. and y = 12sint! N = neti cost (-2,0) (2,0) And Che paramelnie interval is (0, ut e Toste un It starts from (20) at which t-o to (-2,0) to complete Cha haif crcle Counterclovewire where tall, 2nd time (-2,0) to (2002 [il, 21) 3rd time (20) to (-2,0) [20, 31] 4th time (-2,0] to (201! [ 32, Mic]