A particle executes S.H.M., the graph of velocity as a function of displacement is :-

$v^{2}=\omega^{2}\left(A^{2}-x^{2}\right)$

$\frac{v^{2}}{\omega^{2}}+x^{2}=A^{2}$

$\frac{v^{2}}{(\omega A)^{2}}+\frac{x^{2}}{A^{2}}=1$

This is an equation of an ellipse.