L and L¹  are the ends of the latusrectum  of the parabola x² = 6y. The equation of OL and OL¹ where O is the origin is 

$$\begin{gathered} \mathrm{Given} \mathrm{parabola} {\mathrm{x}}^2=6\mathrm{y} \\ \mathrm{where} 4\mathrm{a}=6\Rightarrow \mathrm{a}=\frac{3}{2} \\ Now end points of latusrectum are \\ \mathrm{L}\left(2\mathrm{a}{,}_{ }\mathrm{a}\right) and {\mathrm{L}}^1(-2{\mathrm{a}}_{ },\mathrm{a}) \\ \mathrm{Eq}uation \mathrm{of} \mathrm{OL} \Rightarrow \mathrm{y}=\frac{1}{2}\mathrm{x} \\ \Rightarrow \mathrm{x}-2\mathrm{y}=0, \\ \mathrm{Eq}uation of {\mathrm{OL}}^1 is \mathrm{x}+2\mathrm{y}=0 \\ \mathrm{combined} \mathrm{eq}uation is {\mathrm{x}}^2-4{\mathrm{y}}^2=0 \end{gathered}$$