两定点A(-2,-1),B(2,1)动点P在抛物线y=x^2上移动,则△PAB的垂心G的轨迹方程是
问题描述:
两定点A(-2,-1),B(2,1)动点P在抛物线y=x^2上移动,则△PAB的垂心G的轨迹方程是
答
G(x,y)k(AB)=0.5k(AB)*k(PG)=-10.5*(y-yP)/(x-xP)=-1xP=x+0.5y-0.5yPk(PB)*k(AG)=-1[(yP-1)/(xP-2)]*[(y+1)/(x+2)=-1(1+y)yP =2x+y+5-(2+x)xP=2x+y+5-(2+x)*(x+0.5y-0.5yP)yP=xP=yP=(xP)^2