A particle executes S.H.M., the graph of velocity as a function of...

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

$\dfrac{{v}^{2}}{{\omega}^{2}} + {x}^{2} = {A}^{2}$
$\dfrac{{v}^{2}}{{\left(\omegaA\right)}^{2}} + \dfrac{{x}^{2}}{{A}^{2}} = 1$

This is an equation of an ellipse.