A chord is drawn from a point $P(1,t)$ to the parabola $y^2=4x$, which cuts the parabola at $A$ and $B$. If $PA\cdot PB=3|t|$, what is the maximum possible value of $|t|$?
All I can infer is that the point must be outside the parabola, so $t^2-4\gt 0$, and since cases will become mirror images the moment we make $t$ negative, then $t$ must be greater than $2$.
Taking out actual points and solving (by using parametric form) seems lengthy. Any hint would be appreciated.