A parametric curve of the formx = a cot t + b cost, y = a + b sin t (0 <t< 2)is called a

Chapter 10, Problem 21

(choose chapter or problem)

A parametric curve of the form

\(x=a \cot t+b \cos t, \quad y=a+b \operatorname{sint} \quad(0<t<2 \pi)\)

is called a conchoid of Nicomedes (see the accompanying figure for the case \(0<a<b\)).

(a) Describe how the conchoid

\(x=\cot t+4 \cos t, \quad y=1+4 \sin t\)

is generated as t varies over the interval \(0<t<2 \pi\).

(b) Find the horizontal asymptote of the conchoid given in part (a).

(c) For what values of t does the conchoid in part (a) have a horizontal tangent line? A vertical tangent line?

(d) Find a polar equation \(r=f(\theta)\) for the conchoid in part (a), and then find polar equations for the tangent lines to the conchoid at the pole.

Equation Transcription:

Text Transcription:

x=a cot t+b cos t

y=a+b sint

(0 < t < 2pi)

0 < a < b

x = cot t + 4 cos t

y = 1 + 4 sin t

r = f(theta)