Suppose AB is a focal chord of the parabola y2 = 12x of length ℓ and slope m<3. If the distance of the chord AB from the origin is d, then ℓd2 is equal to __________.

ℓ=4acosec2⁡θℓ=12×9d2ℓd2=108

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Suppose AB is a focal chord of the parabola y² = 12x of length $ℓ$ and slope $m < \sqrt{3}$ . If the distance of the chord AB from the origin is d, then $ℓ d^{2}$ is equal to __________.

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answer is 108.

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$\begin{array}{l} ℓ = 4 {acosec}^{2} θ \\ ℓ = 12 \times \frac{9}{d^{2}} \\ ℓ d^{2} = 108 \end{array}$

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