From a variable point P on the tangent at the vertex of the parabola y 2 = 2 x , a line is drawn perpendicular to the chord of contact. These variable lines always pass through a fixed point, whose x -coordinate is

Step-by-step solution

Comparing the given parabola with y 2 = 4 a x , we get a = 1 2 Equation of the chord of contact of P 0 , λ is λ y = 2 a x i.e. 2 a x - λ y = 0 … i A line perpendicular to it is λ x + 2 a y = c Since it passes through 0 , λ ⇒ 0 + 2 a λ = c ∴ λ x + 2 a y - 2 a λ = 0 λ x - 2 a + 2 a y = 0 x - 2 a + 2 a λ y = 0 Passes through 2 a , 0 i.e. 1 , 0