L1:x−2y+10=0
L2:x+2y−6=0
What is the ratio in which the point of intersection of line L1 and L2 divides the line segment AB of L1?
Let the point of intersection of L1 and L2 be C(x,y)
x−2y+10=0 -------- (1)
x+2y−6=0----------(2)
Solving (1) and (2) simultaneously we get
x=−2
y=4
C≡(−2,4)
Let the ratio in which C divides AB be k: 1
−2=8k−6k+1
−2(k+1)=(8k−6)
−2k−8k=2−6
−10k=−4
5k=2
k=25
The required ratio is 2 : 5