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The ordinate of the centroid of the triangle formed by conormal points on the parabola $y^{2} = 4 a x$ is

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answer is B.

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Detailed Solution

Equation of the normal at t is $y + x t = 2 a t + a t^{3}$

$t_{1} + t_{2} + t_{3} = 0$

The ordinate of the centroid of the triangle at is $t_{1}, t_{2}, t_{3}$ is $\frac{2 a t_{1} + 2 a t_{2} + 2 a t_{3}}{3}$

$\frac{2 a}{3} (t_{1} + t_{2} + t_{3}) = 0$

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