Explanation Graph: Consider the parametric equations, x = 1 t − 1 …… (1) And, y = t + 1 t − 1 …… (2) Convert the above equation in the rectangular equation by elimination method as, Simplify the equation (1) as, x 2 = 1 ( t − 1 ) t − 1 = 1 x 2 t = 1 x 2 + 1 = 1 + x 2 x 2 Substitute 1 + x 2 x 2 for t in equation (2) as, y = 1 + x 2 x 2 + 1 1 + x 2 x 2 − 1 = 1 + 2 x 2 1 + x 2 − x 2 = 2 x 2 + 1 1 = 2 x 2 + 1 Thus, the required rectangular equation is y = 2 x 2 + 1 . The rectangular equation is defined for all the values of x , while the parametric equation is defined, when t − 1 > 0 , which implies that t is greater than 1 , thus, restricting the rectangular equation for positive values

10th Edition

ISBN: 9781337278461

Author: Ron Larson

Publisher: Cengage Learning

See similar textbooks

Concept explainers

Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magn…

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.

Question

Chapter 6.6, Problem 2ECP

To determine

To graph: The curve represented by the equations, x=1t−1 and y=t+1t−1, by eliminating the parameters and adjusting the domain of the rectangular equation.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 6.6, Problem 1ECP

Chapter 6.6, Problem 3ECP

Students have asked these similar questions

To approximate the length of a marsh, a surveyor walks x = 400 meters from point A to point B. Then, the surveyor turns 75° and walks 220 meters to point C (see figure). Approximate the length AC of the marsh. (Round your answer to one decimal place.) m C B 75° 220 m x m

. The students who attend Memorial High School have a wide variety of extra-curricular activities to choose from in the after-school program. Students are 38% likely to join the dance team; 18% likely to participate in the school play; 42% likely to join the yearbook club; and 64% likely to join the marching band. Many students choose to participate in multiple activities. Students have equal probabilities of being freshmen, sophomores, juniors, or seniors.What is the probability of the union of being either a freshman or senior? 0.07 0.44 0.50 0.25

Which angles are complementary to each other? Select all that apply. 3 2 4 in 5 1 Z1 and 23 Z1 and 25 22 and 23 Z2 and 25 Submit

Chapter 6 Solutions

Trigonometry (MindTap Course List)

Ch. 6.1 - Find the inclination of (a) 4x5y=7 and (b) x+y=1.Ch. 6.1 - Prob. 2ECP Ch. 6.1 - Prob. 3ECP Ch. 6.1 - Find the distance between the point 3,2 and the...Ch. 6.1 - Prob. 5ECP Ch. 6.1 - Prob. 1E Ch. 6.1 - Prob. 2E Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E Ch. 6.1 - Prob. 5E

Knowledge Booster

$Trigonometry$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, trigonometry and related others by exploring similar questions and additional content below.

To graph: The curve represented by the equations, x = 1 t − 1 and y = t + 1 t − 1 , by eliminating the parameters and adjusting the domain of the rectangular equation.

Solution Summary: The author explains how to draw a graph of the equations by eliminating the parameters and adjusting the domain.

Concept explainers

To graph: The curve represented by the equations, x=1t−1 and y=t+1t−1, by eliminating the parameters and adjusting the domain of the rectangular equation.

Want to see the full answer?

Chapter 6 Solutions