If the normals at two points $P$ and $Q$ of a parabola $y^2 = 4x$ intersect at a third point $R$ on the parabola $y^2 = 4x$, then the product of the ordinates of $P$ and $Q$ is equal to
Step-by-Step Solution
Key Concept: For a parabola $y^2 = 4ax$, the product of ordinates of two points whose parameters satisfy a given condition equals the product of the parameters scaled by the coefficient.
From $t = -x - 2$, we have $t_1, t_2$ as roots of $x^2 + t x + 2 = 0$. Thus $t_1 t_2 = 2$. The ordinates of $P$ and $Q$ are $2t_1$ and $2t_2$ respectively. The product of ordinates is $(2t_1)(2t_2) = 4t_1 t_2 = 4(2) = 8$.
Correct Answer: 8