Chapter 10.3, Problem 100E

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Chapter
Section

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
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+acosÎ¸y=k+bsinÎ¸

Differentiate x=h+acosÎ¸ with respect to Î¸, to get,

dxdÎ¸=âˆ’asinÎ¸

Differentiate y=k+bsinÎ¸ with respect to Î¸, to get,

dydÎ¸=bcosÎ¸

Horizontal asymptote exist when dxdÎ¸=0

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