Focus = (4, 4) and vertex = (3, 2)

$$\therefore$$ Point of intersection of directrix with axis of parabola = A = (2, 0)

Image of A(2, 0) with respect to line x + 2y = 6 is B(x₂, y₂)

$$\therefore$$ $${{{x_2} - 2} \over 1} = {{{y_2} - 0} \over 2} = {{ - 2(2 + 0 - 6)} \over 5}$$

$$\therefore$$ $$B({x_2},\,{y_2}) = \left( {{{18} \over 5},{{16} \over 5}} \right)$$.

Point B is point of intersection of direction with axes of parabola P₂.

$$\therefore$$ $$x + 2y = \lambda $$ must have point $$\left( {{{18} \over 5},{{16} \over 5}} \right)$$

$$\therefore$$ $$x + 2y = 10$$