If the focal chord drawn through the point (1,2) to the parabola y^2=8 x meets this parabola in (x₁, y₁ ) and (x₂, y₂ ) then x₁+x₂=

Step-by-step solution

Given parabola is y ^2=8 x with parametric coordinates ( at ₁^2, 2 at ₁ ) and ( at ₂^2, 2 at ₂ ) . Let ( x ₁, y ₁ ) (a t ₁^2, 2 a t₁ ) and ( x ₂, y ₂ ) (a t₂^2, 2 a t₂ ) Equation of line passing through ( x ₁, y ₁ ) and ( x ₂, y ₂ ) is ( y -2 at ₁ ) aligned & = 2 a t₂-2 a t₁ a t₂^2-a t₁^2 (x-a t₁^2 ) & (y-2 a t₁ )= 2 (t₂+t₁ ) (x-a t₁^2 ) aligned Satisfy (1,2) , aligned & (2-2 a t₁ )= 2 (t₂+t₁ ) (1-a t₁^2 ) & (1-a₁ )= 1 (t₂+t₁ ) (1-a₁^2 ) & (1-a t₁ ) (t₂+t₁ )= (1-a t₁^2 ) & t ₂+t₁- at ₁ t ₂- at ₁^2=1- at ₁^2 aligned