It can be solved with convex hull trick. For a fixed point, try to rearrange the formula to make it work.

First of all, we find lower convex envelope. Then we can run ternary search. It's the simplest way to do it. For max you would find upper convex envelope instead. If constraints would allow coordinates to be negative you would split points by their x(<0 and >=0) and do two queries.

Try problem squad from function cup 2019 it uses this concept but is a bit harder.

X1*x2+y1*y2=sqrt(x1^2+y1^2)*sqrt(x2^2+y2^2)*cos(a)

a is angle between vectors (x1, y1) and (x2, y2). |(x1,y1)|*|(x2,y2)| * cos(a) = (projectio)^2

This can be done with convex hull of dots and some binary search(lower hull for P.y>0 and upper hull for P.y<0)

P.s sorry for my poor english

I know a trendy question on this concept. ;)