JEE Math Practice Question

For all $$z \in C$$ on the curve $$C_{1}:|z|=4$$, let the locus of the point $$z+\frac{1}{z}$$ be the curve $$\mathrm{C}_{2}$$. Then :

1. A.the curves $$C_{1}$$ and $$C_{2}$$ intersect at 4 points
2. B.the curve $$C_{2}$$ lies inside $$C_{1}$$
3. C.the curve $$C_{1}$$ lies inside $$C_{2}$$
4. D.the curves $$C_{1}$$ and $$C_{2}$$ intersect at 2 points