Question

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

• A. x = 0
• B. y = 0
• C. x = -a
• D. y = a

Answer 1

Answer: (B)

We know that, the sum of ordinates of feet of normals drawn from a point to the parabola, $y^{2}=4 a x$ is always zero.
Norv, as normals at three points $P, Q$ and $R$ 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 $P_{1} Q$ and $R$.
$\Rightarrow y$-coordinates $y_{1},\, y_{2},\, y_{3}$ of these points $P, Q$ and $R$ will be zero.
$\Rightarrow y$-coordinate of the centroid of $\Delta P Q R$
$i.e., \frac{y_{1}+y_{2}+y_{3}}{3}=\frac{0}{3}=0$
Hence, centroid lies on $y=0$.