It will pass through the focus (a,0).

It is a property of the parabola.

Ohh..I'm sorry i got confused between another property...

Yeah the answer is (4a,0)...

As a penalty for wrong answer, I'll write the solution here....

Let co-ordinates of A and B be (at₁²,2at₁) and (at₂²,2at₂).  [t₁ and t₂ are parameters]

They lie on the parabola, evidently.

Slope of OA=2/t₁

Slope of OB=2/t₂

Therefore, (2/t₁)*(2/t₂)=(-1)

or, t₁t₂=(-4)

Now equation of line joining AB is

(t₁+t₂)y=2(x+at₁t₂)     (You can derive it..)

Putting t₁t₂=-4,

(t₁+t₂)y=2(x-4a)

Therefore it always is satisfied by (4a,0).

 answer is [4a,0]