Given that \( (x,y) \) is a point, \( r \) is the length of a line segment joining the origin to that point, \( \theta \) is the angle between the line segment and the line \( y=0 \) and the following three equations:

\( x=a \cos\left( {\omega t} \right)+\sqrt{a^2-b^2} \)

\(y=b \sin\left( {\omega t} \right) \)

\(r^2 \equiv x^2+y^2\)

Find seperate expressions for \( x \) and \( y \) in terms of \( \theta \), \( a \) and \( b \)

Note: \( \theta \) is not always equal to \( \omega t \)

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