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Offline Centres

$P N$ is an ordinate of the parabola $y^{2} = 4 a x$ ( $P$ on $y^{2} = 4 a x$ and $N$ on x-axis). A straight line is drawn parallel to the axis to bisect $N P$ and meets the curve in $Q$ . $N Q$ meets the tangent at the vertex $A$ in a point $T$ such that $A T = k \cdot N P$ , then the value of $k$ is (where $A$ is the vertex)

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$\frac{2}{3}$

$1$

$\frac{3}{2}$

$\frac{1}{3}$

answer is B.

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Detailed Solution

Consider the figure

Observing the above graph $A T = \frac{4 a t}{3} . N P = 2 a t$

Therefore, $k = \frac{2}{3}$

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