A particle moves in the the `x-y` plane according to the scheme `x= 8 sin pit` and y=-2 cos(^2)pit` pit`, where t is time. Find equation of the path of the particle. Show the path on a graph.

Options

A. `y=-2+(x^(2))/16`
B. `y^(2)=-2+(x^(2))/16`
C. `x^(2)=-2+(y^(2))/16`
D. `x=-2+(y^(2))/16`

Answer

A

Explanation

`y=2 cos 2 pi t=-2(12 sin pit)`
`rArr y=-2(1-2((-x)/(8))^(2))`
`rArr y= -2 + (x^(2))/(16)`.