A particle is acted simultaneously by matually perpendicular simple harmonic motion `x=a"cos "omegat` and `y=a "sin"omegat` . 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^(2)+y^(2)=a^(2)[cos^(2)omegat+sin^(2)omegat]` `Rightarrow` `x^(2)+y^(2)=a^(2)`, which is equation of a circle.