   Chapter 10.3, Problem 36E

Chapter
Section
Textbook Problem

# Horizontal and Vertical Tangency InExercises 35-42, find all points (if any) of horizontal and vertical tangency to the curse. Use a graphing utility to confirm your results. x = 4 cos 2 θ , y = 2 sin θ

To determine

All the points of horizontal & vertical tangency to the curve. Verify the result by the use of graphing utility.

Explanation

a) Given:

x=4cos2θ......(1)y=2Sinθ......(2)

b) Calculation:

Differentiate both the functions with respect to θ,

dxdθ=8cosθsinθ & dydθ=2cosθ

For Vertical tangency equate dxdθ=0,

8cosθsinθ=0

Either cosθ=0 or sinθ=0.

θ=±π2&θ=0,π

For Horizontal tangency equate dydθ=0,

cosθ=0θ=±π2

When θ=0, then x=4,y=0.

When θ=π, then x=4,y=0

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