A particle is acted simultaneously by mutally perpendicular simple harmonic motion `x=acosomegat` and `y=asinomegat`. The trajectory of motion of the particle will be

Options

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

Answer

C

Explanation

Given, `x=acosomegat…..(i)`
`y=asinomegat.....(ii)`
Squaring and adding Eqs. (i) and (ii),
`x^(2)+y^(2)=a^(2)` `(cos^(2)omegat+sin^(2)omegat)`
`=a^(2)rArrx^(2)+y^(2)=a^(2)` `[:.cos^(2)omegat+sinomegat=1]`
This is the equation, of a circle
Clearly, the locus is a circle of constant radius a.