Chapter 10: Q. 20. (page 694)

In problem graph the curve whose parametric equations are given and show its orientation. Find the rectangular equation of each curve. Verify your graph using a graphing utility.
$x = 2 \cos t, y = 3 \sin t; 0 \leq t \leq π$

Short Answer

Expert verified

The equation is $\frac{x^{2}}{4} + \frac{y^{2}}{9} = 1 .$

Step by step solution

Step 1. Given information.

$x = 2 \cos t, y = 3 \sin t$ is given.

Step 2. Calculation.

Graph the curve defined by the parametric equations -

$t$	$x$	$y$	$(x, y)$
$0$	$2$	$0$	$(2, 0)$
$π$	$2$	$0$	$(2, 0)$
$\frac{π}{2}$	$0$	$3$	$(0, 3)$
$\frac{π}{4}$	$\frac{2}{\sqrt{2}}$	$\frac{3}{\sqrt{2}}$	$(\frac{2}{\sqrt{2}}, \frac{3}{\sqrt{2}})$

We find the rectangular equation by eliminating the parameter t from the parametric equations.

$x = 2 \cos t y = 3 \sin t \sin t = \frac{y}{3}$

Now, put these value in identity-

$\cos^{2} t + \sin^{2} t = 1 {(\frac{x}{2})}^{2} + {(\frac{y}{3})}^{2} = 1 \frac{x^{2}}{4} + \frac{y^{2}}{9} = 1$

Thus, the equation is $\frac{x^{2}}{4} + \frac{y^{2}}{9} = 1 .$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

In problem graph the curve whose parametric equations are given and show its orientation. Find the rectangular equation of each curve. Verify your graph using a graphing utility.
$x = 2 \cos t, y = 3 \sin t; 0 \leq t \leq π$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Calculation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Theoretical and Mathematical Physics

Applied Mathematics

Statistics

Probability and Statistics

Pure Maths

Study anywhere. Anytime. Across all devices.

In problem graph the curve whose parametric equations are given and show its orientation. Find the rectangular equation of each curve. Verify your graph using a graphing utility.x=2cost,y=3sint;0≤t≤π

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Calculation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Theoretical and Mathematical Physics

Applied Mathematics

Statistics

Probability and Statistics

Pure Maths

Study anywhere. Anytime. Across all devices.

In problem graph the curve whose parametric equations are given and show its orientation. Find the rectangular equation of each curve. Verify your graph using a graphing utility.
$x = 2 \cos t, y = 3 \sin t; 0 \leq t \leq π$