Let PQ be the latus rectum of the parabola y² = 4x with vertex ‘A’ minimum length of the projection of ‘PQ’ on a tangent drawn in portion of the parabola PAQ in

P¹Q¹= projection of PQ on the tangent
Tangent at$\text{ 't'; }\mathrm{yt}=\mathrm{x}+{\mathrm{at}}^2$
Eqⁿ of latus rectum, x =1
$\cos \mathrm{\theta }=\frac{1}{\sqrt{1+{\mathrm{t}}^2}}$ where $\mathrm{\theta }$ is angle between tangent and latus rectum
$\begin{array}{l}{\mathrm{P}}^1{\mathrm{Q}}^1=\mathrm{PQcos}\mathrm{\theta }\\ =4\times \frac{1}{\sqrt{1+{\mathrm{t}}^2}}\mathrm{also}(\mathrm{t}<1)\\ \frac{4}{\sqrt{2}}=2\sqrt{2}\end{array}$