A particle is acted simultaneously by mutually perpendicular simple hormonic motions `x=acos omegat and y =asinomegat.` The trajectory of motion of the particle will be

Options

A. an ellipse
B. a parabola
C. a circle
D. a straight line

Answer

C

Explanation

`x=acosomegat` and `y=asinomegat`
`:.` `x^(2)+y^(2)=a^(2)(cos^(2)omegat+sin^(2)omegat )=a^(2)`
It is an equation of a circle. Thus trajectory of motion of the particle will be circle.