.过点A(-1,-6)的直线L与抛物线y^2=4相交于P,Q两点,若果N(9/2,0)满足/pN/=/QN/,求直线l的

设直线L：y+6=k(x+1),PQ的中点C
xC=(xP+xQ)/2,yC=(yP+yQ)/2
x=(6+y-k)/k
y^2=4x=4*(6+y-k)/k
ky^2-4y+4k-24=0
yC=(yP+yQ)/2=2/k
xC=(6+2/k-k)/k=(2+6k-k^2)/k^2
k(NC)=(2/k)/[(2+6k-k^2)/k^2-9/2]=4k/(4+12k-11k^2)
PQ⊥NC
k(L)*k(NC)=-1
k*4k/(4+12k-11k^2)=-1
k=2,-2/7
直线L的方程有两条:
1,2x-y-4=0
2,2x+7y+44=0