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22 Mar 2020
: Different Ways of Tracing Out a Curve. The curves C, D, E, and F are defined parametrically as follows, where the parameter t takes on all real values unless otherwise stated:
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Show that the points on all four of these curves satisfy the same rectangular coordinate equation.
: Different Ways of Tracing Out a Curve. The curves C, D, E, and F are defined parametrically as follows, where the parameter t takes on all real values unless otherwise stated:
Show that the points on all four of these curves satisfy the same rectangular coordinate equation.
Collen VonLv2
27 May 2020