Let PQ be the latus rectum of the parabola $y = 4x$ with vertex A. Minimum length of the projection of PQ onto a tangent drawn in portion of parabola $PAQ$ answer is $2\sqrt{2}$.
I have tried drawing the diagram but couldn't get the proper understanding of the problem. I tried approaching it with vectors.
Firstly, I made two vectors, dot them both and finally differentiate but couldn't get the answer (I have assume angle between them as $\theta$). Any hints on how to approach this problem would be much appreciated.