If s=a `sinomegat hati+b cos omegat hatj`, the equation of path of particle is

Options

A. `x^(2)+y^(2)=sqrt(a^(2)+b^(2))`
B. `(x^(2))/(b^(2))+(y^(2))/(a^(2))=1`
C. `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1`
D. None of these

Answer

C

Explanation

Here, x= a sin `omegat`
`therefore" "sin omegat=(x)/(a)`
Similarly, `y=b cos omega t`
`therefore" "cos omega t=(y)/(b)`
`therefore" "sin^(2)omegat+cos^(2)omegat=(x^(2))/(a^(2))+(y^(2))/(b^(2))`
`therefore" "(x^(2))/(a^(2))+(y^(2))/(b^(2))=1` (Ellipse)