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and
)
... Start with the given parametric equations.
)^2)
and
)^2)
... Square both sides for each equation.
)
and
)
... Square the right sides and simplify
)
and
)
... Isolate for
)
and
)
.
=\frac{x^2}{4})
and
=\frac{y^2}{16})
Rearrange the equations
Now remember,
=\sec^2(t))
is an identity
... Start with the given identity
... Plug in
and
... Subtract
from both sides.
Rearrange the equation.
Now the equation is in rectangular form
Note: the last equation is in the form of a hyperbola.
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