抛物线y+2x^2上两点A(x1,y1)B(x2,y2)关于直线y=x+m对称且x1*x2=-1/2,则m等于
问题描述:
抛物线y+2x^2上两点A(x1,y1)B(x2,y2)关于直线y=x+m对称且x1*x2=-1/2,则m等于
答
因为AB⊥直线,AB直线斜率k=-1
→y1-y2=x2-x1,根据y1-y2=2x1?-2x2?→x1 x2=0①
AB中点M[(x1 x2)/2,(y1 y2)/2]一定在直线y=x m上
→(y1 y2)/2=(x1 x2)/2 m②,y1 y2=2x1? 2x2?③
②③→x1 x2 2m=2(x1? x2?)④
已知x1x2=-1/2⑤
①④⑤→x1=…x2=…m=…(自己可算出)