Why Are Planetary Orbits Elliptical?

[SandeshPhy]

Why are the orbits of planets revolving around a body(say the sun) elliptical rather than circular or any other shape?
Please show the answer mathematically.

 

[phyzguy]

This page shows how Kepler's laws(including Kepler's first law that planetary orbits are ellipses) follow from Newton's laws of motion and Newton's law of universal gravitation.

http://en.wikipedia.org/wiki/Keplers_laws