Q. 2 - Calculus | StudyQuestionHub

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Q. 2

Question

Sketching parametric equations: Sketch the curves defined by the given sets of parametric equations. Indicate the direction of motion on each curve.

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

Step-by-Step Solution

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Answer

The required graph is as follows, and its increasing upward.

1Step 1. Given Information.

The equations are $x = 3 t + 1$ and $y = - 2 t + 3$ such that $t \in [0, 1]$ .

2Step 2. Explanation.

Using equations, make a table that contains the coordinates of several points on the curve.

t	0	1
$x = 3 t + 1$	1	4
$y = - 2 t + 3$	3	1

3Step 3. Find the direction.

The direction of motion along the parametric curve with increasing values of t. So it is upward increasing.

The required graph is as follows,

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