Precalculus

9th Edition

ISBN: 9780321716835

Author: Michael Sullivan

Publisher: Addison Wesley

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Question

Chapter 10.7, Problem 13AYU

To determine

The graph of the curve of a parametric equation $x=3t2, y=t+1 ; −∞<t<∞$ , show its orientation. Find the rectangular equation of curve.

Expert Solution & Answer

Answer to Problem 13AYU

Solution:

The graph of the parametric equations $x=3t2, y=t+1 ; −∞<t<∞$ is

Precalculus, Chapter 10.7, Problem 13AYU , additional homework tip 1

The rectangular equation of the parametric equation $x=3t2, y=t+1 ; −∞<t<∞$ is $x=3(y−1)2$ .

Explanation of Solution

Given information:

The parametric equation $x=3t2, y=t+1 ; −∞<t<∞$

Explanation:

To draw the given parametric equation, plug some values of $t$ in the given equation and find few points on the curve.

The interval for $t$ is $−∞<t<∞$

$tx(t)=3t2y(t)=t+1(x,y)−212−1(12,−1)−130(3,0)001(0,1)132(3,2)3274(27,4)$

The orientation is curve traced out in a certain direction by the corresponding succession of points $(x,y)$ .

The arrow shows the orientation along the curve as $t$ varies from $−∞<t<∞$

As $t$ takes values from $−∞<t<∞$ , the corresponding orientation is from $(12,−1)$ to $(27,4)$

Use points in the table to sketch the curve.

The graph of the parametric equation $x=3t2, y=t+1 ; −∞<t<∞$ is

Precalculus, Chapter 10.7, Problem 13AYU , additional homework tip 2

Now, let $x=3t2$ ——- (1)

$y=t+1$ ——- (2)

Solve equation (2) for variable $t$ ,

$⇒t=y−1$

Substitute this result for $t$ into equation (1),

$⇒x=3(y−1)2$

The rectangular equation of the parametric equation $x=3t2, y=t+1 ; −∞<t<∞$ is $x=3(y−1)2$ .

Chapter 10.7, Problem 12AYU

Chapter 10.7, Problem 14AYU

Chapter 10 Solutions

Precalculus

Ch. 10.2 - The formula for the distance d from P 1 =( x 1 , y...Ch. 10.2 - To complete the square of x 2 4x , add_______...Ch. 10.2 - Use the Square Root Method to find the real...Ch. 10.2 - The point that is symmetric with respect to the...Ch. 10.2 - To graph y= ( x3 ) 2 +1 , shift the graph of y= x...Ch. 10.2 - _________ is the collection of all points in a...Ch. 10.2 - Prob. 7AYU Ch. 10.2 - Prob. 8AYU Ch. 10.2 - Prob. 9AYU Ch. 10.2 - Prob. 10AYU

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The graph of the curve of a parametric equation x = 3 t 2 , y = t + 1 ; − ∞ < t < ∞ , show its orientation. Find the rectangular equation of curve.

Solution Summary: The author explains how to draw a parametric equation by plugging some values of t in the given equation and finding few points on the curve.

Videos

The graph of the curve of a parametric equation $x=3t2, y=t+1 ; −∞<t<∞$ , show its orientation. Find the rectangular equation of curve.

Answer to Problem 13AYU

Explanation of Solution

Chapter 10 Solutions

Additional Math Textbook Solutions

The graph of the curve of a parametric equation x = 3 t 2 , y = t + 1 ; − ∞ &lt; t &lt; ∞ , show its orientation. Find the rectangular equation of curve.

Solution Summary: The author explains how to draw a parametric equation by plugging some values of t in the given equation and finding few points on the curve.

Videos

Answer to Problem 13AYU

Explanation of Solution

Chapter 10 Solutions

Additional Math Textbook Solutions

The graph of the curve of a parametric equation x = 3 t 2 , y = t + 1 ; − ∞ < t < ∞ , show its orientation. Find the rectangular equation of curve.