If the straight line y = mx + c is parallel to the axes of the parabola y² = lx and intersect the parabola at  $\left(\frac{c^2}{8},c\right)$, the length of latus rectum 

Given parabola $y^2=lx\to \left(1\right)$

$Length of latusrectum=l$

$\text{point}\left(\frac{c^2}{8},c\right)$

Point of intersection  of parabola and line y = mx + c is given  $\left(\frac{c^2}{8},c\right)$

$\text{then \hspace{0.17em}}{c}^2=l\left(\frac{c^2}{8}\right)$

$\Rightarrow$l = 8

$\therefore$L.L¹ = 8