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`.

If a variable line passes through the point of intersectionof the lines x + 2y - 1 = 0 and 2x - y-1 = 0 and meets the coordinate axes in A and B , then the locus of the midpoint of AB is : (A) x + 3y = 0 (B) x + 3y = 10 (C) x + 3y = 10xy (D) None of these

A variable straight line is drawn through the point of intersection of the straight lines x/a+y/b=1 and x/b+y/a=1 and meets the coordinate axes at A and Bdot Show that the locus of the midpoint of A B is the curve 2x y(a+b)=a b(x+y)

A variable straight line is drawn through the point of intersection of the straight lines x/a+y/b=1 and x/b+y/a=1 and meets the coordinate axes at A and Bdot Show that the locus of the midpoint of A B is the curve 2x y(a+b)=a b(x+y)

A straight line through the point of intersection of the lines x + 2y = 4 and 2 x + y = 4 meets the coordinate axes at A and B .the locus of the midpoint of AB is _

A variable straight line is drawn through the point of intersection of the straight lines (x)/(a)+(y)/(b)=1 and (x)/(b)+(y)/(a)=1 and meets the coordinate axes at A and B. Show that the locus of the midpoint of AB is the curve 2xy(a+b)=ab(x+y)

A variable line through the point of intersection of the lines x/a+y/b=1 and x/b+y/a=1 , meets the co-ordinate axes in A and B, then the locus of mid point of AB is

A variable straight line drawn through the point of intersection of the straight lines x/a+y/b=1 and x/b+y/a=1 meets the coordinates axes at A and B. Show that the locus of the mid point of bar(AB) is 2(a+b)xy=ab(x+y) .

A straight line through the point of intersection of the lines x+2y = 4 and 2x +y =4 meets the coordinates axes at A and B. The locus of the midpoint of AB is