6. [40.18 Points] DETAILS SCALCET9 10.1.017. 0(100 Submissions Used MY NOTES ASK YOUR TEACHER Consider the following. x = 83:. y = as: (a) Eliminate the parameter to nd a Cartesian equation of the curve. i: ([3) Sketch the curve and indicate with an arrow the direction in which the curve is traced as the parameter increases. y y 5 5 4 4 3 3 2 2 1 1 Need Help? 11. [-10.18 Points] DETAILS SCALCET9 10.XP.1.024. DH 00 Submissions Used MY NOTES ASK YOUR TEACHER Suppose that the position of one particle at time t is given by x1 = 4 5in(t), y1 = 2 cos(t), 0 s t S 27: and the position of a second particle is given by x2 = 4 + cos(t), y2 = 1 + sin(t), 0 s t s 21:. (5!) Graph the paths of both particles. y 0 How many points of intersection are there? [:1 points of intersection (b) Are any of these points of intersection collision points? That is, are the particles ever at the same place at the same time? If so, nd the collision points. (Enter your answers as a comma-separated list of ordered pairs of the form (x, y). If there are no collision points, enter DNE.) (XI Y) = (c) Describe what happens if the path of the second particle is given by x2 = 4 + cos(t), Y2 = 1 + 5in(t), 0 s t s 21:. The circle is centered at (x, y) = ( ). There are [:J intersection point(s), and there are [2 collision point(s). Need Help? _ Wewing Saved Work Revert to Last Respgnse 9. [-10.18 Points] DETAILS SCALCET9 10.XP.1.027. Oil 00 Submissions Used MY NOTES ASK YOUR TEACHER Find parametric equations for the path of a particle that moves along the circle described by x2 + (y 2)2 = 16 in the manner described. (Enter your answer as a comma-separated list of equations. Let x and y be in terms of t.) (a) Once around clockwise, starting at (4, 2). o s t s 21:. C (b) Two times around counterclockwise, starting at (4, 2). 0 s t S 42:. C (c) Halfway around counterclockwise, starting at (0, 6). 0 s t 5 7;. Z Need Help? 10. [-10.18 Points] DETAILS SCALCET910.1.051. 01100 Submissions Used MY NOTES ASK YOUR TEACHER Ifa and b are xed numbers, nd parametric equations for the curve that consists of all possible positions of the point P in the figure, using the angle 9 as the parameter. (Enter your answer as a comma-separated list of equations. Let x and y be in terms of 9.) '17 +977+77 --+-+661 Eliminate the parameter. S Identify the curve. 0 parabola O hyperbole Viewing Saved Work Revert to Last Rssmnss