For problems 1 9 eliminate the parameter for the given set of
parametric equations, sketch the graph of the parametric curve and give any
limits that might exist on x and y.
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10. Answer each of the questions about the following set of
parametric equations
(a) Sketch
the graph of the parametric curve for .
(b) Sketch
the graph of the parametric curve for .
(c) Sketch
the graph of the parametric curve for .
(d) In
general, for ,
how does the value of a affect the
graph of the parametric curve?
For problems 11 21 the path of a particle is given by the set
of parametric equations. Completely
describe the path of the particle. To
completely describe the path of the particle you will need to provide the
following information.
(i) A sketch of the parametric curve
(including direction of motion) based on the equation you get by eliminating
the parameter.
(ii) Limits on x and y.
(iii) A range of t’s for a single trace of the parametric curve.
(iv) The number of traces of the curve
the particle makes if an overall range of t’s
is provided in the problem.
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For problems 22 27 write down a set of parametric equations
for the given equation that meets the given extra conditions (if any).
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24. and the parametric curve resulting from the
parametric equations should be at when and the curve should have a clockwise rotation.
25. and the parametric curve resulting from the
parametric equations should be at when and the curve should have a counter clockwise
rotation.
26. and the
parametric curve resulting from the parametric equations should be at when and the curve should have a counter clockwise
rotation.
27. and the parametric curve resulting from the
parametric equations should be at when and the curve should have a clockwise
rotation.
28. Eliminate the parameter for the following set of
parametric equations and identify the resulting equation.