Explanation Given information: The given polar equation is r = − 6 cos θ . Formula used: Write the expression for relation between Cartesian and polar equations as follows: x = r cos θ y = r sin θ r 2 = x 2 + y 2 tan θ = y x Calculation: Rewrite the given polar equation as follows: r = − 6 cos θ Multiply with r on both sides of the expression as follows: r 2 = − 6 r cos θ From the relation between Cartesian and polar equations, substitute x for r cos θ and ( x 2 + y 2 ) for r 2 to find the Cartesian equation for the given polar equation. x 2 + y 2 = − 6 x Rewrite the obtained Cartesian equation as follows: x 2 + y 2 + 6 x = 0 ( x + 6 x + 3 2 ) 2 + y 2 − 3 2 =

Thomas' Calculus: Early Transcendentals (14th Edition)

14th Edition

ISBN: 9780134439020

Author: Joel R. Hass, Christopher E. Heil, Maurice D. Weir

Publisher: PEARSON

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Chapter 11, Problem 32PE

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Find the Cartesian equation for the given polar equation and sketch the circle in the coordinate plane and label with both its Cartesian and polar equations.

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Chapter 11, Problem 31PE

Chapter 11, Problem 33PE

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Chapter 11 Solutions

Thomas' Calculus: Early Transcendentals (14th Edition)

Ch. 11.1 - Finding Cartesian from Parametric...Ch. 11.1 - Finding Cartesian from Parametric...Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Prob. 6E Ch. 11.1 - Prob. 7E Ch. 11.1 - Prob. 8E Ch. 11.1 - Finding Cartesian from Parametric...Ch. 11.1 - Finding Cartesian from Parametric...

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