Question

Eliminate the parameter.

x = 4 cos t, y = 4 sin t

Answer 1

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...

Answer 2

Notice that \[x = 4\cos t \Rightarrow x^2 = 16\cos^2 t\]

Answer 3

Also, \[y = 4\sin t \Rightarrow y^2 = 16\sin^2 t \]

Answer 4

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!

Answer 5

\[x^2 + y^2 = 16\]

Answer 6

Any questions? That was a pretty tricky method. @egbeach

Answer 7

Thank you!

Answer 8

No problem. Good luck!