In the parabola y^{2}=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\sqrt{3}). 2. The perpendicular distance of P from the directrix of parabola is 8 units. Select the correct answer using the code given below :

Explanation

For y^2 = 8x, 4a = 8 \implies a = 2. The focal distance of P(x,y) is x+a = x+2. Given x+2 = 8 \implies x = 6. Substituting x=6 into the equation gives y^2 = 48 \implies y = \pm 4\sqrt{3}. Thus, (6, 4\sqrt{3}) is a valid coordinate for P (Statement 1 is true). By the fundamental definition of a parabola, the focal distance of any point equals its perpendicular distance from the directrix (Statement 2 is true).

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