# Elliptical trajectory

If a particle's trajectory is defined by the law x=acos[pt] and y=bsin[pt] where t is parameter of time then we have to prove that it's acceleration vector passes through the focus of the conic----ellipse in this case as can be clearly seen.
If we write out the position vector in the vector notation and differentiate twice we get a=-p2r and this clearly is directed towards the centre of the axes system and not the focus.Any ideas?

D H
Staff Emeritus