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Q66.

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Precalculus Mathematics for Calculus

Found in: Page 593

Book edition 7th Edition

Author(s) James Stewart, Lothar Redlin, Saleem Watson

Pages 948 pages

ISBN 9781337067508

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Short Answer

Polar Equations to Rectangular Equations
Convert the polar equation to rectangular coordinates
$r = \frac{2}{1 - \cos θ}$

The rectangular equation is $y^{2} = 4 (1 + x)$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information

An equation is given in polar coordinate system as $r = \frac{2}{1 - \cos θ}$

Step 2. Concept used

To convert rectangular coordinates to polar coordinates, use the formulae below-

$\begin{array}{l} r = \sqrt{x^{2} + y^{2}} \\ θ = \tan^{- 1} (\frac{y}{x}) \end{array}$

Convert polar coordinates using the same formulas-

$\begin{array}{l} x = r \cos θ \\ y = r \sin θ \end{array}$

Substitute the value in the formulae. And simplify them.

Step 3. Calculation

The polar equation is given as, $r = \frac{2}{1 - \cos θ}$

Multiply by r on both sides,

$\begin{array}{l} r^{2} = \frac{2 r}{1 - \cos θ} \\ \Rightarrow r^{2} = \frac{2 r^{2}}{r - r \cos θ} \\ \Rightarrow 1 = \frac{2}{r - r \cos θ} \\ \Rightarrow 1 = \frac{2}{r - x} \\ \Rightarrow r = x + 2 \\ \Rightarrow r^{2} Invalid <m:msup> element = \\ \Rightarrow x^{2} + y^{2} = x^{2} + 4 + 4 x \\ \Rightarrow y^{2} = 4 (1 + x) \end{array}$

Most popular questions for Math Textbooks

Rectangular Equations to Polar Equations

Convert the equation to polar form. $y = x^{2}$

Testing for Symmetry Test the polar equation for symmetry to the polar axis, the pole, and the line $θ = π / 2$

$r = 5 \cos θ \csc θ$ .

We can describe the location of a point in the plane using different _________systems. The point shown in the figure has rectangular coordinates (_,_) and polar coordinates (_,_)

Plotting Points in Polar Coordinates Plot the point that has the given polar coordinates $(- 5, - \frac{17 π}{6})$

Polar Equations to Rectangular Equations

Convert the polar equation to rectangular coordinates

$\cos 2 θ = 1$

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