P是C:y=1/2x^2上一点,直线l过点P且与抛物线在P处的切线垂直,l与抛物线C交于Q

设P(m,m^2/2)
y`=x→切线斜率k=m
l的斜率为-1/m
→y-m^2/2=-(x-m)/m①
Q(2,2)带入→(m+2)(m-2m-2)=0
→m=k=-2,或者m=k=±√3+1
(2):令M(x,y),P(m,m^2/2)
→Q(2x-m,2y-m^2/2),将其分别带入抛物线,直线y-m^2/2=-(x-m)/m①
→(2x-m)^2/2=2y-m^2/2②,2y-m^2=(2m-2x)/m③
②③→(x^2-1)/x=(m^2-1)/m
→x=m④
③④→y=x^2/2

1) -X +4