已知两点M(-1,0),N(1,0),且点P使MP*MN,PM*PN,NM*NP成公差小于零的等差数列.

题目

已知两点M(-1,0),N(1,0),且点P使MP*MN,PM*PN,NM*NP成公差小于零的等差数列.
若点P坐标为(X0,y0),Q为PM与PN的夹角,求tanθ

答案

M(-1,0),N(1,0),P(x,y).MP*MN=(x+1,y)*(2,0)=2x+2,PM*PN=(-1-x,-y)*(1-x,-y)=x^2+y^2-1,NM*NP=(-2,0)*(x-1,y)=2-2x.依题意,(2x+2)+(2-2x)=2(x^2+y^2-1),且2x+2>2-2x；即x^2+y^2=3且x>0.则cosQ=(PM*PN)/(|PM|*|PN|)=(...