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A variable straight line passes through the points of intersection of the lines `x +2y= 1` and `2x-y = 1` and meets the co-ordinates axes in `A` and `B`. Prove that the locus of the midpoint Of `AB` is `10xy = x + 3y`.

A

`2x-3y=4`

B

`(2)/(x)-(3)/(y)=6`

C

`x+3y=10xy`

D

`x+y=xy`

Text Solution

Verified by Experts

The correct Answer is:
A

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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