求轨迹?已知A(-1,0),B(2,0),使

Question

求轨迹?
已知A(-1,0),B(2,0),使

Answer 1

∠PBA=2∠PAB
P(x,y)
k(PB)=y/(x-2)
k(PA)=y/(x+1)
过B作BC平分∠PBA,交PA于C ,则∠CBA=∠CBP=∠PAB
k（BC）=-k（PA）=-y/(x+1)
∠CBA=∠CBP
{y/(x-2)-[-y/(x+1)}/{1+[y/(x-2)]*[-y/(x+1)]}=-y/(x+1)
3x^2-y^2=3
点P的轨迹:x^2-y^2/3=1