Question

已知抛物线y方=4X,过点P(4,0)的实现与抛物线教育A(x1,y1),B(x2,y2)两点,求x1的倒数+x2的倒数

Answer 1

过点P(4,0)的直线：x=my+4

与抛物线联立得y^2-4my-16=0

y1+y2=4m,y1y2=-16

1/x1+1/x2=4/y1^2+4/y2^2

=4(y1^2+y^2)/(y1y2)^2

=4[(y1+y2)^2-2y1y2]/(y1y2)^2

=4*(16m^2+32)/16^2

=m^2/4+1/2

当m=0,(1/x1+1/x2)min=1/2