# Conics, Parametric Equations, and polar Coordinates

Answers must be explained very clearly. Answers without proper justification will not be accepted. I am having a lot of trouble with these questions and the last time I posted this the TA just gave me a bunch of BS. Please take your time and answer these questions clearly and accurately with step by step work so I can follow along. Thanks and have fun.

Question 1

Given the polar function r = 2 - 2cos

a) Find the parametric equations for the function (i.e., x=....'s, y=...'s.)

b) Find the derivative, dy/dx

c) Find all vertical tangent lines and singular points

Question 2

Given the two polar equations r1 = 2 - 2cos and r2 = 3

a) Find the values of where r1 intersects r2 (Please show graph)

b) Find the arc length or r1 on the interval 's found in part a.

c) Set up the integral to find the area of the surface of revolution for the segment of r1 on the same interval of 's found in part a when rotated about the pole (x-axis).

d) Set up the integrals to find the area of the region bounded on the left by r1 and on the right by r2

Resources:

I am using the book Calculus, Larson, Hostetler, and Edwards, Seventh edition.

https://brainmass.com/math/calculus-and-analysis/conics-parametric-equations-polar-coordinates-28332

#### Solution Summary

The expert examines conic, parametric equations and polar coordinates. The expert finds the value of intersects and intervals.