[" EXAMPLE 64If a variable line drawn through the intersection of "],[" the lines "(x)/(3)+(y)/(4)=1" and "(x)/(4)+(y)/(3)=1," meets the coordiantes axes at "A],[" and "B," then the locus of the mid-point of "AB," is "],[" (a) "7xy=6(x+y)" ."]

A variable straight line through the point of intersection of the two lines (x)/(3)+(y)/(2)=1and(x)/(2)+(y)/(3)=1 meets the coordinate axes at A and B . Find the locus of the middle point of AB.

If a variable line drawn through the intersection of the lines (x)/(3)+(y)/(4)=1 and (x)/(4)+(y)/(3)=1 meets the coordinate axes at A and B,(A!=B) ,then the locus of the midpoint of AB is (A) 6xy=7(x+y)(B)4(x+y)^(2)-28(x+y)+49=0(C)7xy=6(x+y)(D)14(x+y)^(2)-97(x+y)+168=0

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 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 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 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 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 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) .