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

The point of intersection of the lines x/a+y/b=1 and x/b+y/a=1 lies on

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)

The point of intersection of the lines x/ay/b =1 and x/b +y/a =1 lines on the line

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

The point of intersection of the lines (x)/(a)+(y)/(b)=1 and (x)/(b)+(y)/(a)=1 lies on the plane