在平面直角坐标系xOy中,点P到两点（0,负根号3）,（0,根号3）的距离之和等于4,设点P的轨迹为C

1.4>2√3,可知C为椭圆,焦点在y轴上.
c=√3,a=1,b=2.
C：x^2+y^2/4=1.
2.代入y=kx+1得4x^2+(kx+1)^2=4整理得(4+k^2)x^2+2kx-3=0.
又,向量OA垂直向量OB,设A:(x1,y1),B:(x2,y2),(x1>x2)
得x1*x2+y1*y2=0,
x1*x2=-3/(4+k^2),yi*y2=k^2*x1*x2+k(x1+x2)+1=-3k^2/(4+k^2)-2k^2/(4+k^2)+1=(4-k^2)/(4+k^2),
得(1-k^2)/(4+k^2)=0,
k=±1,
得5x^2±2x-3=0,
(x1-x2)^2=(x1+x2)^2-4x1*x2=64/25,
|AB|=√[(k^2+1)*(x1-x2)^2]=8√2/5