Homework 27 – Parametric Equations 1) Express in the form yfxby eliminating the parameter. a) 3, 4xtyt b) 24,6ttxeye c) ln , 2xty t d) 2cos , sinxty t 2) Graph the parametric curves. Include arrows indicating the direction of motion. a) ,tt t b) ,ttee t c) 21,22xty t d) 2cos , sin 0 2xty tt 3) A particle follows the trajectory 3212, 204xtttyt tt, with t in seconds and distance in centimeters. X is the horizontal distance and y is the vertical distance.a) What is the particle’s maximum height? b) When does the particle hit the ground and how far from the origin does it land? 4) Find parametric equations for the given curve. a) Line through (3, 1) and (‐5, 4). b) 2yx , translated so that the minimum occurs at (‐4, ‐8). c) Circle of radius 4 with center (3, 9). 5) Find a parametrization c(t) of the curve satisfying the given condition. a) 34, 0 2,2yx c b) 34, 3 2,2yx c c) 2,03,9yx c 6) The graphs of x(t) and y(t) as functions of t are shown in Figure A. Which of a‐c is the plot of ,ct xt yt? 7) Find the points on the curve 2332,6ct t tt t where the tangent line has slope 3. 8) Find the equation of the tangent line to the cycloid generated by a circle of radius 4 at 2t. 9) Find 22dydx at t = 1 for 214xtytt 10) Find the t‐intervals on which 23,4ct t t tis concave up. 11) Let ,ct xt yt, where y(t) > 0 and '0xt. Then the area under c(t) for atb is 'baAytx tdt. Find the area under one arch of the cycloid 5 5sin ,5 5cosct t t t
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