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A curve is described by the following parametric equations: x=3+ y= t2-4 Which statement best describes the curve? (1 point) O The curve is a parabola with a vertex at (3, 4) and is traced from left to right for increasing values of t. O The curve is a parabola with a vertex at (3, 4) and is traced from right to left for increasing values of t. O The curve is a parabola with a vertex at (3,4) and is traced from left to right for increasing values of t. O The curve is a parabola with a vertex at (3,4) and is traced from right to left for increasing values of t. Which points are on the plane curve described by the following set of parametric equations? Select all that apply. x=3t+4and y= 22 (1 point) 0O (1-2) 0 (12) O (17) 0 (210) 0 (7.2) Consider the Cartesian equation of a circle, y = -2+,{36- (x1)2 , versus the parametric equations of the same circle: x=1+6cost y=-2+6sn, What are the advantages of the parametric equations? Select all that apply. (2 points) (J The parametric equations show the direction in which the circle is drawn. (J The parametric equations describe a three-dimensional figure. (J For a given value of the independent variable, the parametric equations yield exactly one point on the graph. (J The parametric equations have a finite domain. (J The parametric equations are easier to enter into a calculator for graphing. \fWhich is the graph of the following parametric equation? x = vi and y = 2t + 1 (1 point) 5 t= 2 t= 1 t = 0 O X -5 5 -5\f\fRewrite the following parametric equations in rectangular form. x:e3' and _)J'='_r (1 point) What is the shape of the graph of the following parametric equations? x = 3 cos t and y = 2 sin t + 1 (1 point) O circle O ellipse O hyperbola O parabolaWhich equation in rectangular form describes the parametric equations x=5-3cost andy =4 + 2 sin t? (1 point) 2 2 o G397, o+4? 9 4 (+4)? (x+5 _ 2 3 1 o U= -5 _, 2 3 Which set of parametric equations represents the function y = x + 2x-3? Select all that apply. (1 point) X=t+1 0 y = 12 + 2t X = 2t y = 412+41-3 x=t-3 O y = 1 + 2t x =/2 0 y = 2t - 3 x =t+1 O y =1 +41Identify the parametric equations that represent the same graph as the following parametric equations. Select all that apply. x =3t y=t*+1 (1 point) x =2t y=462+1 x =2t 1, =t"+2 7732 Identify the parametric equations that represent the same path as the following parametric equations. X = 4 + cos 0 y = 3 sin 0 (1 point) X = cos 0 y = 4 + 3 sin 0 X = 4 + 2 cos 0 y = 6 sin 0 O X = 4 + cos 40 y = 3 sin 40 OX = 3 sin 0 y = 4 + cos 0Which statement describes the graph and orientation of the parametric equations x = 4 cos t and y = 4 sin t? (1 point) (O The graph is a circle with a radius of 2. The orientation is counterclockwise as t increases. O The graph is a circle with a radius of 2. The orientation is clockwise as t increases. O The graph is a circle with a radius of 4. The orientation is counterclockwise as t increases. O The graph is a circle with a radius of 4. The orientation is clockwise as t increases. Which is the parametric form of the polar equation = =387 (1 point) x=308cos b8 O y=30sin0 x=-38co0s 8 y=-38s5n8 x=-3cos8 O y=-3s1mn8 x=-8cos 8 O y=-8sind Which is the polar form of the parametric equations x = 5 cos 0 and y = 5 sin 0? (1 point) Or = 50 Or=5 O r = 25 cos 0 sin 0 Or = 25cos2 8+ 25sin2 8Which is the polar form of the parametric equations x = 4t and y = 2? (1 point) O r = 16 tan 0 sec 0 Or = 16tan2 8 Or = 16 sec2 8 Or = 16 sec 0A bowling ball is rolled down the alley with a constant velocity of 1.5 m/sec. at an angle of 87 to the starting line. The position of the person throwing the bowling ball can be represented by the point (0,0). Where is the ball after 7 seconds? (1 point) O (0.5,10.5) O (0.1,1.5) O (10.5,10.5) O (29,200 A ball is thrown with a slingshot at a velocity of 110 ft./sec. at an angle 20 above the ground from a height of 4.5 ft. Approximately how long does it take for the ball to hit the ground? Acceleration due to gravity is 32 ft /s2. (1 point) (O 2.35 seconds O 2.47 seconds O 6.46 seconds O 6.50 seconds Use the graph to answer the question. Which set of parametric equations represents the graph of the function shown? t = 1.57 (1 point) O x = 2.5 cos t and y = 1.5 sin t O x = 10 cos t and y = 6 sin t t= 0 x -6 -5 -4 -3 -2 -1,0 1 2 3 4 5 6 O x = 5 cos t and y = 3 sin t O x = 5 sin t and y = 3 cos tThe following two sets of parametric functions both represent the same ellipse. Explain the difference between the graphs. x = 3 cos t and y = 8 sin t x = 3 cos 4t and y = 8 sin 4t (4 points) BIExplain how you would graph the following set of parametric equations by plotting points and describing the orientation. x = 3t and y = 2 (4 points) B IFor parametric equations x = a cos t and y = b sin t, describe how the values of a and b determine which conic section will be traced. (2 points)