w2014 activity on 4.8-- intro to parametric equations - 4....

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4.8  Introduction to Parametric Equations1.Write a set of parametric equations that describes the path of each particle.a.Particle A starts at the point ( 2 , 3 ) and traces out a circle with center ( 2 , 0 ) and radius 3, completing four counterclockwise revolutions in 24 seconds.Step 1.Label the x and y coordinates of the points at the 12 o'clock, 3 o'clock, 6 o'clock, and 9 o'clock positions along with the corresponding times.Step 2.Sketch one period of the graph of the x coordinate as a function of time. Then, use the graphto find an equation for x ( t ).Step 3.Repeat step 2for the y coordinate and so find y ( t ).Step 4.Remember to include bounds on t as part of your answer. ( e.g. ___ <t <____ )b.Particle B starts at the point ( 4 , 0 ) and traces out an ellipse with center ( 0 , 0 ), horizontal major axis length = 8, and vertical minor axis length = 6, completing one clockwiserevolution in 10 seconds.c.Particle C starts at the point ( - 3 , 1 ) and traces out a line segment which ends at ( 4 , 5 ) after one second.d.Particle D starts at the point ( - 3 , 1 ) and traces out a line segment which ends at ( 4 , 5 ) after five seconds.e.Particle E traces out a line which passes through the points ( – 3 , 1 ) and ( 4 , 5 ).f.Particle F traces out the portion of the parabola x = y 2– 4 between the points ( – 3 , – 1 ) and ( 5 , 3 ).Step 1.Let y = t.Step 2.Substitute y = t into the given equation in order to obtain x in terms of t.Step 3.Write the set of equations. [ TIP: