= Solution
For <elliptical polarization from circular and linear components>, use coherent waves of the same <frequency>, propagation direction and fixed relative phase. Let the circular component be $A(\widehat{\mathbf x}\cos\psi+\widehat{\mathbf y}\sin\psi)$ and the linear component $B\widehat{\mathbf x}\cos\psi$, with $A,B>0$. Their sum has $E_x=(A+B)\cos\psi$ and $E_y=A\sin\psi$, so
$$
\boxed{\frac{E_x^2}{(A+B)^2}+\frac{E_y^2}{A^2}=1}.
$$
The tip of the <electric field> traces an ellipse with unequal semiaxes $A+B$ and $A$. Coherence is necessary: averaging unrelated phases does not create this fixed <polarization ellipse>.
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