Give a parametrization for each of the following curves. Sketch the graph of each curve, showing...

  

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Give a parametrization for each of the following curves. Sketch the graph of each curve, showing the direction (orientation). a. A line segment from (-3,1) and (5,4), with 0sts 10. b. The function y=x-x+3. c. A circle centered at (4,-2) with radius 5. d. The ellipse centered at (5,-1) that passes through the points (2,-1), (5,4), (8,-1), (5,-6). Parameterize so that t=0 corresponds to the point (5, 4) and the ellipse is traversed clockwise over 0 Sts 1. 2. The motion of a particle is given by x=,y = t, over time-2 st 2. a. Sketch the graph of the parametric curve. Show the direction (or orientation) of the curve. b. Find expressions for the position, velocity and acceleration of the curve as vectors. c. Find an expression for the speed of the particle in terms of t. What happens to the speed over the journey over time-2sts 2? Does the particle ever come to a stop? d. Eliminate the parameter and express the curve as an equation relating x and y. (HINT: After eliminating the parameter, graph your equation to make sure that it indeed gives the same graph asx =t, y = t. Give a parametrization for each of the following curves. Sketch the graph of each curve, showing the direction (orientation). a. A line segment from (-3,1) and (5,4), with 0sts 10. b. The function y=x-x+3. c. A circle centered at (4,-2) with radius 5. d. The ellipse centered at (5,-1) that passes through the points (2,-1), (5,4), (8,-1), (5,-6). Parameterize so that t=0 corresponds to the point (5, 4) and the ellipse is traversed clockwise over 0 Sts 1. 2. The motion of a particle is given by x=,y = t, over time-2 st 2. a. Sketch the graph of the parametric curve. Show the direction (or orientation) of the curve. b. Find expressions for the position, velocity and acceleration of the curve as vectors. c. Find an expression for the speed of the particle in terms of t. What happens to the speed over the journey over time-2sts 2? Does the particle ever come to a stop? d. Eliminate the parameter and express the curve as an equation relating x and y. (HINT: After eliminating the parameter, graph your equation to make sure that it indeed gives the same graph asx =t, y = t.