Let there be two parabolas y 2 = 4 x and y 2 = - 8 x . Then the locus of the mid-points of the intercepts between the parabolas made on the lines parallel to the common axis is

Step-by-step solution

Let line parallel to common axis be y = h . Then coordinates of A and B are h 2 4 , h and - h 2 8 , h respectively. If P ≡ α , β , then α = 1 2 h 2 4 - h 2 8 ,   β = h ⇒ 2 α = h 2 4 1 1 - 1 2 = h 2 8 ∴ Locus of P is x = y 2 16