   Chapter 11.7, Problem 89E

Chapter
Section
Textbook Problem

# Converting a Rectangular EquationIn Exercises 79–86, convert the rectangular equation to an equation in (a) cylindrical coordinates and (b) spherical coordinates. x 2 − y 2 = 9

(a)

To determine

To calculate: Rectangular and Cylindrical coordinates are given. Calculate the equation in cylindrical coordinates for the surface represented by the rectangular equation x2y2=9.

Explanation

Given:

The rectangular equation is:

x2y2=9

Formula used:

Conversion formula is:

x2+y2=r2tanθ=yx

Calculation:

Rectangular coordinates to cylindrical coordinates,

x2+y2=r2

tanθ=yx

Rectangular equation is x2y2=9.

1+tan2θ=1+y2x21+sin2θcos2θ=x2+y2x2sin2θ+cos2θcos2θ=x2+y2x21cos2θ=x2+y2

(b)

To determine

To calculate: Spherical and Cylindrical coordinates are given. Calculate the equation in spherical coordinates for the surface represented by the rectangular equation x2y2=9.

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