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.

Question

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. (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.

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/c9bbede7db6d4d5fd99e89a8be10b752-.png" /> Let AB be a focal chord. Slope of AB =(2 t / t 2-1)= tan α ⇒ tan (α/2)=(1/ t ) ⇒ t = cot (α/2) Length of AB = a ( t +(1/ t ))2=4 a cosec2 α ⇒ Reason is correct but Assertion is false.

Q. Assertion : Length of focal chord of a parabola $y^{2} = 8 x$ making an angle of $6 0^{\circ}$ with $x$ -axis is $32$ .
Reason: Length of focal chord of a parabola $y^{2} = 4$ ax making an angle $α$ with $x$ axis is $4 a cose c^{2} α$ .

Assertion is correct, reason is correct; reason is a correct explanation for assertion.

Assertion is correct, reason is correct; reason is not a correct explanation for assertion

Assertion is correct, reason is incorrect

Assertion is incorrect, reason is correct.

Let $A B$ be a focal chord.
Slope of $A B = \frac{2 t}{t ^{2} - 1} = tan α$
$\Rightarrow tan \frac{α}{2} = \frac{1}{t}$
$\Rightarrow t = cot \frac{α}{2}$
Length of $A B = a (t + \frac{1}{t})^{2} = 4 a cose c^{2} α$
$\Rightarrow$ Reason is correct but Assertion is false.

Q. Assertion : Length of focal chord of a parabola y2=8x 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 4acosec2α.