[Physics] General Relativity & Kepler’s law

general-relativitygravityorbital-motion

According to Kepler's law of planetary motion, the earth revolves around the sun in an elliptical path with sun at one of its focus.
However,
according to general theory of relativity,
the earth revolves around the sun in the curved space and it revolves in a circular path.

Which is correct? Does the planet moves in a circular path or an elliptical path?

The notion that GR predicts that a planet moves in circular path is not really true. GR is just an extension (though it's complex math) for what we didn't understand over centuries. Not only newtonian mechanics, but any consistent theory that makes use of the inverse-square law uses the conics like parabolas, hyperbolas, ellipses and circles. Depending on the velocity at which the object arrives (comparable to gravity), its orbit can be any of the conics.

Now, this makes sense that any object isn't in elliptical or circular orbit always. It may or may not change, based on the objects it interacts along its path. Here's a simulator on the orbits of celestial objects. There are lot of presets. For instance, you can see the slingshot preset where a planet makes an asteroid to go out of orbit. So, it's not true that all orbits are elliptical always.