Let $A B$ be a chord of the parabola $y^{2} = 4 a x$ .If the pole of $A B$ with respect to the parabola be $(2 a, 3 a)$ then the length of $A B$ is

\sqrt{13} a

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4 a

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5 a

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2 \sqrt{3} a

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Solution

The correct option is B $\sqrt{13} a$
Given pole of AB w.r.t the parabola $y^{2} = 4 a x$ is $(2 a, 3 a)$
Thus the equation of chord $A B$ is given by $T = 0$
$\Rightarrow y (2 a) - 2 a (x + 3 a) = 0$
$\Rightarrow y = \frac{2}{3} x + \frac{4}{3} a$
Clearly here $m = \frac{2}{3}, c = \frac{4}{3} a$
Therefore length of chord AB is $= \frac{4}{m^{2}} \sqrt{a (1 + m^{2}) (a - c m)} = \sqrt{13} a$

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Let AB be a chord of the parabola y2=4ax.If the pole of AB with respect to the parabola be (2a,3a) then the length of AB is

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