Homework 7 - Math 142, Frank Thorne ([email protected])Due Friday, October 11(a) What is a parametric curve? Draw a picture and give an example.(b) Given a curve defined by parametric equationsx=f(t),y=g(t), which variables are functionsof the other variables?(c) Give (and draw) examples of parametric curves that illustrate the following possibilities. Ex-plain thoroughly.•ycan be described as a function ofx.•xcan be described as a function ofy.•Both of the above are true.•Neither of the above are true.(d) Suppose you have a functiony=f(x) that you want to define by parametric equations. Howwould you do it?Could you do it a different way?Is there any limit to the number of ways you could do it?(e) Give parametric equations for a line, a circle, an ellipse (other than a circle), and a parabola.Graph all of your curves.(f) A bug sits on the edge of a bicycle tire while you ride the bicycle, and does not move (relativeto its position on the tire). Assume that the bicycle moves forward at a constant speed and
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