A=(−4,0),B=(4,0) . M and N are the variable points of y-axis such that M lies below N and MN = 4:1. Line joining AM and BN intersect at P, locus of P is

Let M=(0,h) ⇒N=(0,h+4) Equation of AM isx−4+yh=1 ⇒yh=4+x4⇒h=4y4+x Equation of BN isx4+yh+4=1 ⇒yh+4=4−x4 ⇒h+4=4y4−x ⇒h=4y−16+4x4−x ⇒4(y−4+x)4−x=4y4+x (eliminating h)2xy−16+x2=0 , which is  a required locus.