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)`.

Find the point of intersection of the straight lines x/a+y/b=1 and x/b+y/a=1, (a!=+-b)

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

The equation of the straight line passing through the point of intersection of the straight lines x/a+x/b=1 and x/b+y/a=1 and having infinite slope is

The vertical straight line passing through the point of intersection of the straight lines x-3y+1=0, 2x+5y-9=0 and at a distance of 2 units from the origin has the equation

If a circle passes through the points of intersection of the axes with the lines ax-y+1=0 and x-2y+3=0 then a=

Consider a variable line L which passes through the point of intersection P of the line 3x+4y-12=0 and x+2y-5=0 meetingt the coordinate axes at point A and B. Locus of the middle point of the segment AB has the eqution

Consider a variable line L which passes through the point of intersection P of the line 3x+4y-12=0 and x+2y-5=0 meetingt the coordinate axes at point A and B. Locus of the feet of the perpendicular from the origin on the variable line L has the equation