A particle moves in the $x-y$ plane according to the rule $x=a \sin \omega t$ and $y=b \cos \omega t

Question

A particle moves in the $x-y$ plane according to the rule $x=a \sin \omega t$ and $y=b \cos \omega t$ (where $a 
eq b$). The particle follows

Professor PC Thomas Classes · Answer

(a) : $x = a \sin \omega t \implies \frac{x}{a} = \sin \omega t$. \ $y = b \cos \omega t \implies \frac{y}{b} = \cos \omega t$. \ Squaring and adding gives $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$. This is the standard equation of an ellipse.