egbeach
  • egbeach
Eliminate the parameter. x = 4 cos t, y = 4 sin t
Mathematics
chestercat
  • chestercat
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jtvatsim
  • jtvatsim
For most of these questions the strategy is to solve one equation for t and plug this into the remaining equation, however, that will be very messy for this one. Instead, you will need to be a little clever and use the fact that \[\cos^2 t +\sin^2 t = 1. \] Here's how...
jtvatsim
  • jtvatsim
Notice that \[x = 4\cos t \Rightarrow x^2 = 16\cos^2 t\]
jtvatsim
  • jtvatsim
Also, \[y = 4\sin t \Rightarrow y^2 = 16\sin^2 t \]

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jtvatsim
  • jtvatsim
Then, (again being very clever) notice that we can add these new equations together to get \[x^2 + y^2 = 16\cos^2 t + 16 \sin^2 t \] but this is just \[x^2 + y^2 = 16(\cos^2 t + \sin^2 t) = 16(1) = 16 \] There the parameter is gone!
jtvatsim
  • jtvatsim
\[x^2 + y^2 = 16\]
jtvatsim
  • jtvatsim
Any questions? That was a pretty tricky method. @egbeach
egbeach
  • egbeach
Thank you!
jtvatsim
  • jtvatsim
No problem. Good luck!

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