In the parabola y² = 8x, the focal distance of a point P lying on it is 8 units. Which of the following statements is/are correct? 1. The coordinates of P can be (6, 4√3). 2. The perpendicular distance of P from the directrix of parabola is 8 units.

For parabola y² = 8x, 4a = 8 so a = 2; focus is (2, 0) and directrix is x = –2. Focal distance of point (x, y) equals x + a = x + 2. Given focal distance = 8, so x = 6. Then y² = 48, y = ±4√3. So P can be (6, 4√3) — statement 1 is correct. By definition of parabola, focal distance equals perpendicular distance from directrix, so distance from directrix is also 8 units — statement 2 is correct. Both statements are correct.