Two simple harmonic motions, as shown, are at right angles. They are combined to form Lissajous figures
$x\left( t \right) = A\,\sin \,\left( {at + \delta } \right)$
$y\left( t \right) = B\,\sin \,\left( {bt} \right)$
Identify the correct match below
JEE MAIN 2018, Diffcult
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From the two mutually perpendicular $S.H.M. 's$, the general equation of Lissajous figure
$\frac{{{x^2}}}{{{A^2}}} + \frac{{{y^2}}}{{{B^2}}} - \frac{{2xy}}{{AB}}\cos \,\delta = {\sin ^2}\,\delta$
$x = A\,\sin \,\left( {at + \delta } \right)$
$y = B\,\sin \,\left( {bt + r} \right)$
Clearly $A\ne B$ hence ellipse
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