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Chapter 10, Problem 38(choose chapter or problem)
Serpentine Curve Consider the parametric equations \(x=2 \cot \theta\) and \(y=4 \sin \theta \cos \theta, 0<\theta<\pi\).
(a) Use a graphing utility to graph the curve.
(b) Eliminate the parameter to show that the rectangular equation of the serpentine curve is \(\left(4+x^{2}\right) y=8 x\).
Text Transcription:
x=2 cot theta
y=4 sin theta cos theta, 0<theta<pi
(4+x^2)y=8x
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