Suppose $A B$ is a focal chord of the parabola $y^2=12 x$ of length $l$ and slope $\mathrm{m}

Question

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

Aicharya · Accepted Answer

$\begin{aligned} & \ell=4 \mathrm{a} \operatorname{cosec}^2 	heta \ & \ell=12 	imes \frac{9}{\mathrm{~d}^2} \ & \ell \mathrm{d}^2=108\end{aligned}$

Suppose $A B$ is a focal chord of the parabola $y^2=12 x$ of length $l$ and slope $\mathrm{m} < \sqrt{3}$.…

Solution