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Precalculus Mathematics for Calculus
Found in: Page 593
Precalculus Mathematics for Calculus

Precalculus Mathematics for Calculus

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


The rectangular equation isy2=4(1+x)

See the step by step solution

Step by Step Solution

Step 1. Given information

An equation is given in polar coordinate system as r=21cosθ

Step 2. Concept used

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


Convert polar coordinates using the same formulas-


Substitute the value in the formulae. And simplify them.

Step 3. Calculation

The polar equation is given as,r=21cosθ

Multiply by r on both sides,

r2=2r1cosθr2=2r2rrcosθ1=2rrcosθ1=2rxr=x+2r2Invalid <m:msup> element=x2+y2=x2+4+4xy2=4(1+x)

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