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Question

A straight line through the origin O meets the lines 4x+2y=9 & 2x+y+6=0 at point P and Q resp. Then the point O divides the segment PQ in ratio ?

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Solution

Given : Equation of lines are 4x+2y=9 & 2x+y=6
A line passes trough origin meets the given lines at P and Q.
To find the ratio at which origin divides the line joining P and Q.
Let the equation of straight line be y=mx
Intersection of lines :
4x+2y=9..........(1)
y=mx........(2)
2x+y=6...........(3)
y=mx............(4)
On putting values of y from 2 to 1 and from 4 to 3.
4x+2mx=9
x=94+2my=9m4+2m2x+mx=6x=6m2+my=6m2+m
Let origin divide PQ in m:1
P(94+2m,94+2m)Q(6m2+m,6m2+m)Q=m(9m4+2m)+(6m2+m)1m+19m4+2m=6m2+m18m+9m2=2412mm=43
Therefore origin divides PQ in the ratio of 4:3 externally.

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