   Chapter 10, Problem 6RE

Chapter
Section
Textbook Problem

# Use the graphs of x = f(t) and y = g(t) to sketch the parametric curve x = f(t), y = g(t). Indicate with arrows the direction in which the curve is traced as t increases. To determine

To find: The parametric curve figure from the given equations.

Explanation

Given:

Equations are x=f(t) and y=g(t)

Calculation:

Consider the equation x=f(t) .

The figure shows the curve for the equation x=f(t) as shown in the figure (1).

From the above figure shows parabola curve where the variable t is in the limit of ±1

Therefore,

f(t)=k(t+1)(t1)

f(t)=k(t21) (1)

From the figure, f(0)=1

Substitute 0 for t in the equation (1).

f(t)=k(t21)f(0)=k(021)

f(0)=k(1) (2)

Calculate the value of k.

Substitute 1 for f(0) in the equation (2).

f(0)=k(1)1=k(1)k=1

Substitute 1 for k in the equation (1).

f(t)=k(t21)f(t)=1(t21)f(t)=t21

Assume t21=x . Therefore,

t21=xt=±x+1 (3)

Consider the equation y=g(t) .

From the above figure shows the polynomial curve where the variable t is 0,±1

Therefore, the equation is,

g(t)=k(t1)t(t+1) (4)

g(t)=kt(t21) (5)

From the graph, take t as 0

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