   Chapter 10.3, Problem 100E

Chapter
Section
Textbook Problem

True or False ? In Exercises 97-100, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.The curve given by x = h + a cos θ and y = k + b sin θ has two horizontal asymptotes and two vertical asymptotes.

To determine
The statement “The curve given by x=h+acosθ and y=k+bsinθ has

two horizontal asymptotes and two vertical asymptotes” is true or false.

Explanation

Consider the given equations,

x=h+acosθy=k+bsinθ

Differentiate x=h+acosθ with respect to θ, to get,

dxdθ=asinθ

Differentiate y=k+bsinθ with respect to θ, to get,

dydθ=bcosθ

Horizontal asymptote exist when dxdθ=0

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