a
Two perpendicular $S.H.Ms$ are
$x=a_{1} \cos \omega t$ $...(1)$
and $y=a_{2} \cos 2 \omega t$ $...(2)$
From eqn $( 1 )$
$\frac{x}{a_{1}}=\cos w t$
and from eqn $(2)$
$\frac{y}{a_{2}}=\cos 2 \omega t=2 \cos ^{2} \omega t-1$
$y=2 \frac{a_{2}}{a_{1}^{2}} x^{2}-1$