Correct Answer - Option 1 : (9, 6√3)

__Concept:__

**A Parabola with equation y2 = 4ax:**

- The focus is at the point (a, 0).
- The general form of any point on the parabola is (at
^{2}, 2at).
- The focal distance of a point is the distance between the point and the focus.

__Calculation:__

The focus of the parabola y2 = 12x = 4(3)x will be at F(3, 0).

Let's say that the required point on the parabola is P(3t^{2}, 6t).

Now, using the distance formula, we have:

PF^{2} = (3t^{2} - 3)^{2} + (6t - 0)^{2}

⇒ 12^{2} = 9(t^{2} - 1)^{2} + 36t^{2}

⇒ 12^{2} = 9(t2 + 1)2

⇒ t = ±√3

So, the required points on the parabola are (9, 6√3) and (9, -6√3).