Book edition 5th

Author(s) Otto Bretscher

Pages 442 pages

ISBN 9780321796974

Answers without the blur.

Just sign up for free and you're in.

Short Answer

Give an example of a parametrization of the ellipse
$x^{2} + \frac{y^{2}}{4} = 1$
in $ℝ^{2}$ . See Example .

$[\begin{matrix} \cos (t) \\ 2 \sin (t) \end{matrix}]$ is a parametrization of the ellipse $x^{2} + \frac{y^{2}}{4} = 1$ in $ℝ^{2}$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Consider the parameters.

The image of a function consists of all the values the function takes in its target space. If f is a function from X to Y, then

$i m a g e (f) = \{f (x : x i n X)\} = \{b i n Y : b = f (x), f o r s o m e x i n X\}$

The standard form of an ellipse is, $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$

The parametrization of this ellipse is,

$x = (a) \cos (t), y = (b) \sin (t) [\begin{matrix} x \\ y \end{matrix}] = [\begin{matrix} (a) \cos (t) \\ (b) \sin (t) \end{matrix}]$

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

The parametrization of this ellipse is,

$x = (1) \cos (t), Y = (2) \sin (t) [\begin{matrix} x \\ y \end{matrix}] = [\begin{matrix} (1) \cos (t) \\ (2) \sin (t) \end{matrix}]$

Step 2: Final answer.

$[\begin{matrix} \cos (t) \\ 2 \sin (t) \end{matrix}]$ is a parametrization of the ellipse $x^{2} + \frac{y^{2}}{4} = 1$ in $ℝ^{2}$ .

Find Study Materials for

Create Study Materials

Select your language

Linear Algebra With Applications

Answers without the blur.

Short Answer

Give an example of a parametrization of the ellipse
$x^{2} + \frac{y^{2}}{4} = 1$
in $ℝ^{2}$ . See Example .

Step by Step Solution

Step 1: Consider the parameters.

Step 2: Final answer.

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Select your language

Linear Algebra With Applications

Answers without the blur.

Short Answer

Give an example of a parametrization of the ellipse x2+y24=1 in ℝ2 . See Example .

Step by Step Solution

Step 1: Consider the parameters.

Step 2: Final answer.

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Decision Maths

Calculus

Probability and Statistics

Statistics

Mechanics Maths

Geometry

Pure Maths

Give an example of a parametrization of the ellipse
$x^{2} + \frac{y^{2}}{4} = 1$
in $ℝ^{2}$ . See Example .