1.

A variable straight line passes through the intersection of x+2y=1,2x-y=1 and meets co-ordinate axes in A and B. The locus of mid-point of AB is :

Answer»

`2x-3y=4`
`(2)/(x)-(3)/(y)=6`
`x+3y=10xy`
`x+y=xy`

Solution :
Let `A(3lambda+7,2lambda+7,lambda+3)`
`B(2k+1,4k-1,3k-1)`
`because` DIRECTION ratios of L are 2,2,1.
`implies(3lambda-2k+6)/(2)=(2lambda-4k+8)/(2)=(lambda-3k+4)/(1)`
`implieslambda=2" and "k=0`
`thereforeA(13,11,5),B(1,-1,-1)`
`implies AB = 18`


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