The normals at three points $P, Q$ and $\mathrm{R}$ of the parabola $y^{2}=4 a x$ meet at $(h, k)$. The centroid of the $\Delta P Q R$ lies on

The sum of ordinates of feet of normals drawn from a point to the parabola, $\mathrm{y}^{2}=4 \mathrm{ax}$ is always zero. Now, as normals at three points $\mathrm{P}, \mathrm{Q}$ and $\mathrm{R}$ of parabola $y^{2}=4 a x$ meet at $(h, k)$. $\Rightarrow$ The normals from $(h, k)$ to $y^{2}=4 a x$ meet the parabola at $\mathrm{P}, \mathrm{Q}$ and $\mathrm{R}$. $\Rightarrow y$-coordinate $y_{1}, y_{2}, y_{3}$ of these points and R will be zero. $\Rightarrow \quad y$-coordinate of the centroid of $\Delta P Q R$ i. e., $\frac{y_{1}+y_{2}+y_{3}}{3}=\frac{0}{3}=0$ $\therefore \quad$ centroid lies on $\mathrm{y}=0$