Elliptical trajectory

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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?
 

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D H
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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.
 
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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.
 

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