JEE Main 2022 — Parabola Question with Solution

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)

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

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

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

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

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