b
$x=a \sin \omega t$
$y=a \sin (\omega t+\pi / 2)=a \cos \omega t$
or, $\quad \frac{x}{y}=\frac{\sin \omega t}{\cos () t}=\tan \omega t$ or, $\frac{x}{y}=\frac{x}{\sqrt{a^{2}-x^{2}}},$
or, $y^{2}=a^{2}-x^{2}$ or, $x^{2}+y^{2}=a^{2}$.
It is an equation of a circle.