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)`.

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 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 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 drawn throgh the point of intersection of the lines x/a+y/b=1,x/b+y/a=1 meets the coordinate axes in A and B. Then the locus of midpoint 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 2 x + y = 4 meets the coordinate axes at A and B .the locus of the midpoint of AB is _