How exactly did the person determine the restrictions of the locus from x = -4(p + 4/p)?
Thanxx a lot!!!
That person may have used the AM-GM inequality: $\displaystyle \frac{x+y}2\geq\sqrt{xy}$ if $\displaystyle x,y\geq0$ with equality iff $\displaystyle x=y$.
Thus $\displaystyle p+\frac 4p\geq2\sqrt{p\times\frac4p}=4$ if $\displaystyle p>0$.
Consequently $\displaystyle p+\frac4p\leq-4$ if $\displaystyle p<0$.