Chapter 10.2, Problem 41E

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Chapter
Section

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

# Eliminating a Parameter In Exercises 39-42, eliminate the parameter and obtain the standard form of the rectangular equation.Ellipse: x = h + a cos θ ,   y = k + b sin θ

To determine

To calculate: The rectangular equation of an ellipse by the elimination of the parametric

equations given as x=h+acosθ,y=k+bsinθ.

Explanation

Given:

The parametric equations of the ellipse are x=h+acosÎ¸,y=k+bsinÎ¸.

Formula used:

The trigonometric identity sin2Î¸+cos2Î¸=1.

Calculation:

The given parameter equations are x=h+acosÎ¸,y=k+bsinÎ¸.

In the equation x=h+acosÎ¸ ;

x=h+acosÎ¸xâˆ’h=acosÎ¸xâˆ’ha=cosÎ¸ â€¦...â€¦... (1)

Similarly, in the equation y=k+bsinÎ¸ ;

y=k+bsinÎ¸yâˆ’k=bsinÎ¸yâˆ’kb=sinÎ¸ â€¦...â€¦..

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started