a
\(\begin{array}{l}
\vec v = k\left( {y\hat i + x\,\hat j} \right) = {v_x}\hat i + {v_y}\hat j = \frac{{dx}}{{dt}}\hat i + \frac{{dy}}{{dt}}\hat j\\
\therefore \frac{{dx}}{{dt}} = ky\,\,\,\,\,and\,\,\,\,\therefore \frac{{dy}}{{dt}} = kx\\
\therefore \frac{{dy}}{{dx}} = \frac{x}{y} \Rightarrow ydy = xdx \Rightarrow {y^2} = {x^2} + {\rm{constant}}
\end{array}\)