Chapter 10.1, Problem 7E

### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336

Chapter
Section

### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336
Textbook Problem

# (a) Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the direction in which the curve is traced as t increases. (b) Eliminate the parameter to find a Cartesian equation of the curve. 7. x = t2 − 3, y = t + 2, −3 ≤ t ≤ 3

(a)

To determine

To plot: The curve using the parametric equations. x=t23 and y=t+2 .

Explanation

Given data:

The parametric equation for the variable x is as follows.

x=t2âˆ’3 (1)

The parametric equation for the variable y is as follows.

y=t+2 (2)

The range of t is âˆ’3 to 3 .

Calculation:

The value of t is increased from âˆ’3 to 3 with a step value of 1 and substituted in the parametric Equations (1) and (2) to obtain the value of x and y respectively.

Substitute âˆ’3 for t in Equation (1).

x=t2âˆ’3=(âˆ’3)2âˆ’3=9âˆ’3x=6

Substitute âˆ’3 for t in Equation (2).

y=t+2=(âˆ’3)+2y=âˆ’1

The values of x and y for each step value of t is tabulated in the below table

(b)

To determine

To find: obtain a Cartesian equation of the curve by eliminating parameter t .

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