Proving Elliptical Trajectory Acceleration Vector Passes Through Focus

[aim1732]

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]

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.

Correct.

Any ideas?

Ideas regarding what? I assume you are trying to prove Kepler's first law. The given equation does not describe a planet's motion. You need to find the right equation.

 

[aim1732]

have to prove that it's acceleration vector passes through the focus of the conic----ellipse in this case as can be clearly seen.

I meant this.