A≡−4,0, B≡4,0. M and N are the variable points of the y-axis such that M lies below N and MN=4. Lines AM and BN intersect at P. The locus of P is

Let M≡0,h. Then or N≡0,h+4The equation of AM is x−4+yh=1or yh+4+x4or h=4y4+xThe equation of BN is x4+yh+4=1or yh+4=4−x4or h+4=4y4−xor h=4y−16+4x4−xor 4y−4+x4−x=4y4+x ( Eliminating h )or 2xy−16+x2=0, which is the required locus