Q. 21. In problem graph the curve whose... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 10: Q. 21. (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.
$x = 2 \cos t, y = 3 \sin t; - 蟺鈮� t 鈮� 0 .$

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 1. Calculation.

Graph the curve defined by the parametric equations -

$t$	$x$	$y$	$(x, y)$
$0$	role="math" localid="1648577233984" $2$	$0$	$(2, 0)$
$- 蟺$	$- 2$	$0$	$(- 2, 0)$
$\frac{- 蟺}{2}$	$0$	role="math" localid="1648577098087" $3$	$(0, 3)$
$\frac{- 蟺}{4}$	role="math" localid="1648577574094" $\frac{2}{\sqrt{2}}$	$\frac{- 3}{\sqrt{2}}$	role="math" localid="1648577593451" $(\frac{2}{\sqrt{2}}, \frac{- 3}{\sqrt{2}})$

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

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

Now, put these value in identity-

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

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91影视

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.
$x = 2 \cos t, y = 3 \sin t; - 蟺鈮� t 鈮� 0 .$

Short Answer

Step by step solution

Step 1. Given information.

Step 1. Calculation.

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91影视

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;-蟺鈮�t鈮�0.

Short Answer

Step by step solution

Step 1. Given information.

Step 1. Calculation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Statistics

Theoretical and Mathematical Physics

Geometry

Discrete Mathematics

Decision 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.
$x = 2 \cos t, y = 3 \sin t; - 蟺鈮� t 鈮� 0 .$