Is the charge on the plates of a parallel plate capacitor induced charge? My question is-

Is the charge on the plates of a parallel plate capacitor induced charge?

Imagine two plates of the capacitor have $+q$ and $-q$ charges on it.
Basically, what I want to know is that if, I earthed (or grounded) one plate of a parallel plate capacitor, would the charge distribution still remain symmetrical (in equal and opposite sense) or would it change? I think that if it is induced charge it would not change otherwise it should change.
Thanks!
 A: 
Imagine two plates of the capacitor have $q$ and $-q$ charges on it.

If both plates have some non-zero net charge, it means that the charge is not induced. Electrostatic induction could cause charge redistribution in a neutral conductor, but the net charge would remain zero.

Basically, what I want to know is that if, I earthed (or grounded) one
  plate of a parallel plate capacitor, would the charge distribution
  still remain symmetrical (in equal and opposite sense) or would it
  change?

Grounding of one of the plates would not change charge distribution. Moreover, if the grounded plate did not have any net charge on it before the grounding, it would attract charge $q$ (positive or negative, depending on the charge sign on the other plate) from the ground to make the capacitor neutral and the distribution of charges would be indistinguishable from the first scenario. 
A: 
Basically, what I want to know is that if, I earthed (or grounded) one plate of a parallel plate capacitor, would the charge distribution still remain symmetrical (in equal and opposite sense) or would it change?

The energy associated with an unbalanced charge tends to be relatively high. Look at all of the matter around you. It consists of positively charged protons and negatively charged electrons but virtually all of the objects around you are electrically neutral because of the large energy penalty associated with having unbalanced charges. So, yes, if you started charging one plate of a parallel plate capacitor with a static electricity generator with the opposite plate connected to ground, then the opposite plate would try to draw in electrons from the ground or expel electrons into the ground in order for the capacitor as a whole to remain electrically neutral and thereby minimize the electrostatic energy of the system. Your attempt to charge up one plate of the capacitor would induce a nearly equal and opposite charge on the opposite plate of the capacitor.
A: Lets make the charges on both plates the same $q,q$. Now ground one of them. What do you expect should happen? The charges on the grounded plate go into ground. Experiencing repulsion from the other like plate, they wish to get as far away as possible. Ground is like infinity, so they go there.
Conversely, when the charges on the plates are opposite, upon grounding, the charges on the plate would stay the same. In fact, instead of grounding, if you put another similar plate between the two and then connect it to any one plate, the charges on that plate would flow onto it.$^1$
In fact the above arguments hold for any pair of conductors in any charge config.
The charges on the plates of a capacitor aren't induced charges in the same sense as imparting temporary charge separation to a conductor via contactless electrostatic induction. That keeps the conductor neutrl. Instead the charging of each plate (while the whole thing stays neutral) is the $work$ of the charging battery. This is not to say that charges on one plate, are independent of the other when the battery has been removed. They bask in each other electric field.
But this point is irrelevant here. How charges got onto the two conductors has no bearing on what those charges will do when one of them is grounded.

$^1$ accompanied by energy loss.
