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)`

The straight line passing through the point of intersection of the straight line x+2y-10=0 and 2x+y+5=0 is

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

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

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 tangent at any point P on the circle x^2+y^2=4 meets the coordinate axes at A and B . Then find the locus of the midpoint of A Bdot

Find the equation to the straight line which passes through the point of intersection of the straight lines x+2y=5 and 3x+7y=17 and is perpendicular to the straight line 3x+4y=10

If the straight line x/a+y/b=1 passes through the line point of intersection of the lines x+y=3 and 2x-3y=1 and is parallel to x-y-6=0 , find a and b.

What is the equation of the straight line which passes through the point of intersection of the straight lines x+2y=5 and 3x+7y=17 and is perpendicular to the straight line 3x+4y=10 ?

Find the equation of the straight line which passes through the point of intersection of the straight lines 3x-4y+1=0 and 5x+y-1=0 and cuts off equal intercepts from the axes.

Find the equation of the straight line drawn through the point of intersection of the lines x+y=4\ a n d\ 2x-3y=1 and perpendicular to the line cutting off intercepts 5,6 on the axes.