The correct option is C 10xy=x+3y
Equation of any line passes through the intersection of x+2y−1=0 and 2x−y−1=0 is (x+2y−1)+λ(2x−y−1)=0 λ is a variable
⇒x(2λ+1)+y(2−λ)−(λ+1)=0
which meet the co - ordinate axes at
A(λ+12λ+1,0) and B(0,λ+12−λ)
Let P(h,k) be the mid point of AB
⇒h=λ+12(2λ+1),k=λ+12(2−λ)
⇒2λ+1λ+1=12h,(2−λ)λ+1=12k
⇒12h+12k=λ+3λ+1
⇒k+h2hk=1+2λ+1⇒2λ+1=k+h−2hk2hk
⇒λ+1=4hkk+h−2hk⇒λ=6hk−k−hh+k−2hk
Now putting the value of λ in h=λ+12(2λ+1)
⇒h=2hk10hk−k−h
⇒10hk=h+3k
∴ locus of P(h,k) is 10xy=x+3y
Hence, option B is the correct answer.