QJEEM22Ma4538: JEE Main 2022 Mathematics - Class 11 JEEM22Ma4538 Solution: Let P 1 be a parabola with vertex (3, 2) and focus (4, 4) and P …

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 $\left( {{{18} \over 5},{{16} \over 5}} \right)$

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