The position vector of a particle P with respect to a stationary point O change with time according to the law `vec(r) = vec(b) sin omega t + vec(c) cos omega t` where `vec(b)` and `vec(c)` are constant vectors with `b pot c` and `omega` is a positive constant. Find the equation of the path of the particle `y = f (x)`, assuming x an dy axes to coincide with the direction of the vector `vec(b)` and `vec(c)` respectively and to have the origin at the point O

Answer

`[(x^(2))/(b^(2)) + (y^(2))/(c^(2)) = 1]`