\(x=a_{1} \cos \omega t\)                    \(...(1)\)

and \(y=a_{2} \cos 2 \omega t\)                \(...(2)\)

From eqn \(( 1 )\)

\(\frac{x}{a_{1}}=\cos w t\)

and from eqn \((2)\)

\(\frac{y}{a_{2}}=\cos 2 \omega t=2 \cos ^{2} \omega t-1\)

\(y=2 \frac{a_{2}}{a_{1}^{2}} x^{2}-1\)