Question

已知两点M(-1,0),N（1,0）且点P使PM*PN=1/2(MP*MN+NM*NP)

Answer 1

1.PM=(-1-x,0-y),PN=(1-x,0-y),MP=(x+1,y-0),MN=(1+1,0-0),NM=(-2,0),NP=(x-1,y)

PM*PN=1/2(MP*MN+NM*NP)-->x^2-1+y^2=2-->x^2+y^2=3

NM*NP-MP*MN-2x+2-2x-2x>0

2.cosa=PN*PM/(|PN||PM|)=1/(根号(4－x^2))-->sina=根号（1－1／（4－x^2））=根号（（3－x^2)/(4-x^2)）-->tana=根号（3－x^2)