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  4. Assertion: Length of focal chord of a parabola y2=8 x making an angle of 60° with x -axis is 32 . Reason: Length of focal chord of a parabola y2=4 ax making an angle α with x axis is 4 a cosec2 α.

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Q. Assertion : Length of focal chord of a parabola $y^{2}=8 x$ making an angle of $60^{\circ}$ with $x$ -axis is $32$ .
Reason: Length of focal chord of a parabola $y^{2}=4$ ax making an angle $\alpha$ with $x$ axis is $4 a \,cosec^{2} \alpha$.

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Solution:

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Let $AB$ be a focal chord.
Slope of $AB =\frac{2 t }{ t ^{2}-1}=\tan \alpha $
$ \Rightarrow \tan \frac{\alpha}{2}=\frac{1}{ t } $
$\Rightarrow t =\cot \frac{\alpha}{2}$
Length of $AB = a \left( t +\frac{1}{ t }\right)^{2}=4 a \,cosec^{2} \alpha$
$\Rightarrow $ Reason is correct but Assertion is false.