   Chapter 10.3, Problem 35E

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 = 5 + 3 cos θ , y = − 2 + sin θ

To determine

All the points of horizontal & vertical tangency to the curve x=5+3cosθ & y=2+sinθ and verify it by the use of graphing utility.

Explanation

Given:

x=5+3cosθ......(1)y=2+sinθ......(2)

Explanation:

Differentiate both the functions with respect to θ,

dxdθ=3sinθ & dydθ=cosθ

For vertical tangency, equate dxdθ=0 and obtain the value of θ

3sinθ=0θ=0,π,2π

For horizontaltangency, equate dydθ=0

dydθ=0cosθ=0=cos(±π2)θ=±π2

θ=±π2

For horizontal tangency

Substitute ±π2 for θ in equation (1) and (2) and obtain the value of x and y,

x=5+3cosπ2=

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started 