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Question

L1:x2y+10=0

L2:x+2y6=0

What is the ratio in which the point of intersection of line L1 and L2 divides the line segment AB of L1?


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Solution

Let the point of intersection of L1 and L2 be C(x,y)

x2y+10=0 -------- (1)

x+2y6=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=8k6k+1

2(k+1)=(8k6)

2k8k=26

10k=4

5k=2

k=25

The required ratio is 2 : 5


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