When a particle executes SHM, the nature of graphical representation of velocity as a function of displacement is:

For a particle executing simple harmonic motion, the displacement is $$x = A\sin(\omega t + \phi)$$ and the velocity is $$v = A\omega\cos(\omega t + \phi)$$.

From the displacement equation, $$\sin(\omega t + \phi) = \frac{x}{A}$$, and from the velocity equation, $$\cos(\omega t + \phi) = \frac{v}{A\omega}$$.

Using the identity $$\sin^2\theta + \cos^2\theta = 1$$, we get $$\frac{x^2}{A^2} + \frac{v^2}{A^2\omega^2} = 1$$.

This is the equation of an ellipse in the $$x$$-$$v$$ plane with semi-major axis $$A$$ along the displacement axis and semi-major axis $$A\omega$$ along the velocity axis. Since in general $$A \neq A\omega$$ (unless $$\omega = 1$$), the graph of velocity as a function of displacement is an ellipse.

The correct answer is elliptical.