   Chapter 10.1, Problem 7E

Chapter
Section
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=t23 (1)

The parametric equation for the variable y is as follows.

y=t+2 (2)

The range of t is 3 to 3 .

Calculation:

The value of t is increased from 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 3 for t in Equation (1).

x=t23=(3)23=93x=6

Substitute 3 for t in Equation (2).

y=t+2=(3)+2y=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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