Question

The point on the parabola y² = 12x, which has a focal distance equal to 12, is:
1. (9, 6√3)
2. (6, 9√3)
3. (-9, 6√3)
4. None of these.

Answer 1

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 (at², 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(3t², 6t).

Now, using the distance formula, we have:

PF² = (3t² - 3)² + (6t - 0)²

⇒ 12² = 9(t² - 1)² + 36t²

⇒ 12² = 9(t2 + 1)2

⇒ t = ±√3

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