Wouldn't the centrifugal/-pedal forces between the planet and Sun make the planet revolve around the Sun in a perfect circle? Is there a 'third force' that attracts planets at a specific point (a hypothetical reasoning for elliptical orbits)?
I need to rant a bit, not at you, Hassaan Qazi, but at whoever taught you (and who teach so many others) that orbits are a balance of a centrifugal force and a centripetal force. There is no third force, and indeed, there is no centrifugal force. There is but one force, gravitation, and it is a central force rather than a centripetal force.
In particular, there is no centrifugal force if you look at the solar system from the perspective of an inertial frame of reference. From this perspective, the solar system comprises a number of planets, asteroids, and other bodies, each of which orbits the Sun at its own orbital velocity. The only force acting on these bodies is gravity.
Each of these objects more or less follows a conic section: A hyperbola, a parabola, an ellipse, or a circle. Some comets are on a hyperbolic or parabolic trajectory. We see them once, and then they are gone forever. The planets and asteroids follow paths that are very close to elliptical. Note that a circle is just a special case of an ellipse. If some planet did have a circular orbit (but none do), it would still be okay to call that planet's orbit elliptical.
I intentionally wrote "more or less" and "very close to" in the above. Those conic sections only arise in the case of the two body problem. Our solar system comprises many bodies. While the Sun is the most influential body gravitationally, planets are gravitationally attracted to other planets as well as to the Sun. If by some fluke a planet was on a perfectly circular orbit, it wouldn't stay that way for long because one of those other planets would perturb it from that perfectly circular orbit.