Hello,

Central force is one in which the direction of the force (attractive or repulsive) is directed towards or away from a fixed point in space, which may be called the centre of the force.

A conservative force is one in which the work done in moving a particle from one point to another depends only on the positions of the two particles and is independent of the path taken while moving the particle.

Now due to certain limitations such as not being able to use mathematical symbols in answers i won't be able to post the proof.

Though you can easily find the solution to your query on web. You just need to open your browser and type your query and you will get a lot of suggestions for mathematical proof of your query.

I hope you find the answer helpful.

Thank you.