Acceleration in ellipse

[prabhat rao]

prove that the acceleration of a body moving with constant speed in ellipse is always directed towards one of the focus .
I have tried but my efforts have gone in vain

 

[Hootenanny]

Can you write me a vector equation for the path of a particle travelling in an ellipse?

 

[HallsofIvy]

Hootnannty indicates our problem! I can think of several ways of doing this, some involving simple but VERY tedious mathematics (I wouldn't want to do it that way!), others involving short calculations but much deeper mathematics. If you don't show us anything of your work (you tell us you have made efforts but don't describe them), we don't know what methods you can use.