Question

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 $4 a \,cosec^{2} \alpha$.

• A. Assertion is correct, reason is correct; reason is a correct explanation for assertion.
• B. Assertion is correct, reason is correct; reason is not a correct explanation for assertion
• C. Assertion is correct, reason is incorrect
• D. Assertion is incorrect, reason is correct.

Answer 1

Answer: (D)

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.