8- 10 Parametric Considering the given value of t, choose the ordered pair that lies on the graph of the given pair of parametric equations. 8) x = -4t + 8, y = 3t - 3; t = -7 B) A) (36, -24) B) (4, 0) C) (-3,-7) D) (20, -18) Give two parametric representations for the equation of the parabola. 9) y = (x+3)2 - 10 9 ) A) x = t, y = (t + 3)2 - 10 for tin (-oo, w.); x = t - 3, y = 12 - 10 for tin (-co, co) B) x = t, y = (t - 3)2 - 10 for t in (-wo, w.); x = t + 3, y = 12 - 10 for tin (-co, co) C) x = t, y = (t + 3)2 - 10 fortin (-oo, @); x= t + 3, y = t2 - 10 fortin (-co, co) D) x = t, y = (t - 3)2 + 10 fortin (-o, "); x = t - 3, y = 12 - 10 fortin (-co, co) Parametric equations and and a parameter interval for the motion of a particle in the xy-plane are given. Identify the particle's path by finding a Cartesian equation for it. Graph the Cartesian equation. Indicate the portion of the graph traced by the particle and the direction of motion. 10) x = 2 cost, y = 2 sint, nest s 2n 10) X-12-0 -2+ -37 We could save A) x2 + y2 = 4; Counterclockwise from B) x2 + y2 = 1; Clockwise from (2, 0) to (2, 0), one rotation (1, 0) to (1, 0), one rotation I right to fof from 3 4 # 3 2 -2+ -34C) x2 + y2 = 4; Counterclockwise from D) x2 + y2 =4; Clockwise from (2, 0) to (-2, 0) (-2, 0) to (2, 0) N 11) 11) x = 4+2, y = 2t, - costs. x = 4+2 7 x= 462 4 = 2+ 42 = 4+2 -DEtex x -4 2= 0 -2 X=yz We could have - 27 (= 4 2 x= 4 ( 4 ) =4 4 A) y = x2; Entire parabola, right to left (from X = yz 1st quadrant to origin to 2nd quadrant) - 3 36 - 6 -2 16 - 4 - 14 - 2 -27 -3+B) y = x2; Entire parabola, left to right (from 2nd quadrant to origin to Ist quadrant) sty 3+ -2+ - 34 C) x = y2; Entire parabola, bottom to top (from 4th quadrant to origin to 1st quadrant) sty 4 43 2 .1. -2+ -3- or the toscaled avis - 5+ D) x = y2; Entire parabola, top to bottom (from 1st quadrant to origin to 4th quadrant) sty B: 89 3 + 72 1h beside the lemniscate 4 -3 -2 -1 Find the length 19, The moral -2+ -3+ -4+ - s+Find an equation for the line tangent to the curve at the point defined by the given value of t. 12) x = t + cost, y = 2 - sin t, t= _ 12) A) y = - 0 18) A) na2 B) a2 C) 0 D) a2 Find the length of the curve. 19) The spiral r= e30, 0 = 0 s n 19) A) 72 (e67 - 1) B) V10 (e37t - 1) C) 8(712 - 1) D) e67 - 3 20) The curve r = 8v1 + sin 20, OsOs-4 20) A) 8(7 + 2) B) 8(7 + In(7 + 2)) C) 2n D) 27V2