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Sketch the curves defined by

the given sets of parametric equations. Indicate the direction

of motion on each curve.
x=3t+1,y=-2t+3,t[0,1]

Short Answer

Expert verified

The required graph is shown below:

Step by step solution

01

Given information

The parametric curves:

x=3t+1,y=-2t+3,t[0,1]

The goal is to draw the parametric curve.

Assume 0,1when drawing the graph for the parametric equations.

Put, e different tvalues in the parametric equations and find the values of

x,y

02

Find the value of (x,y)

Whent=0

(x,y)=(3t+1,-2t+3)

Put t=0and simplify:

(x,y)=(3·0+1,-2·0+3)(x,y)=(1,3)

When t=1

(x,y)=(3t+1,-2t+3)

Put, t=1and simplify:

(x,y)=(3·1+1,-2·1+3)(x,y)=(4,1)

03

The tabular representation of the points is as follows

The table is shown below:

t
0
1
x
1
4
y
3
1
04

Draw a graphical representation with the help of (x,y) values

The required graph is shown below:

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