A particle executes S.H.M., the graph 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, $$\sin(\omega t + \phi) = \frac{x}{A}$$. From the velocity equation, $$\cos(\omega t + \phi) = \frac{v}{A\omega}$$.

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

This is the equation of an ellipse with semi-axes $$A$$ along the $$x$$-axis and $$A\omega$$ along the $$v$$-axis. Therefore, the graph of velocity as a function of displacement is an ellipse.