Answer this question by providing the proper method as soon as possible

Dear student,
To find the locus, we will eliminate the term which contains time. And we will try to find the relation between x and y
$$\begin{gathered} x=a\cos wt, y=a\sin wt \\ \frac{x}{a}= \cos wt, \frac{y}{a}=\sin wt \\ {\left(\frac{x}{a}\right)}^2= {\cos }^{2}wt----1 \\ {\left(\frac{y}{a}\right)}^2= {\sin }^{2}wt----2 \\ adding 1 \& 2, we get: \\ {\left(\frac{x}{a}\right)}^2+{\left(\frac{y}{a}\right)}^2=1 \\ {x}^2+ y^2 = a^2 \\ This is the locus of Circle. \end{gathered}$$
Option 2 is correct.
Regards