Q 2 - Calculus

Question

Sketch the curves defined by

the given sets of parametric equations. Indicate the direction

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

Step-by-Step Solution

Answer

The required graph is shown below:

Step 1: Given information

The parametric curves:

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

The goal is to draw the parametric curve.

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

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

$x,y$

Step 2: Find the value of ( x , y )

When $t=0$

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

Put $t=0$ and simplify:

$$\begin{gathered} (x,y)=(3·0+1,-2·0+3) \\ (x, y)=(1,3) \end{gathered}$$

When $t=1$

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

Put, $t=1$ and simplify:

$$\begin{gathered} (x,y)=(3·1+1,-2·1+3) \\ (x, y)=(4,1) \end{gathered}$$

Step 3: The tabular representation of the points is as follows

The table is shown below:

$t$	$0$	1
$x$	$1$	$4$
$y$	$3$	$1$

Step 4: Draw a graphical representation with the help of ( x , y ) values

The required graph is shown below: