The fix point through which the line `x(a + 2b) + y(a + 3b) = a + b` always passes for all values of `a` and `b`, is-

The point of intersection of the lines x/a + y/b = 1 and x/b + y/a = 1 does not lie on the line

If 5a+5b+20 c=t , then find the value of t for which the line a x+b y+c-1=0 always passes through a fixed point.

The line parallel to the x-axis and passing through the intersection of the lines a x+2b y+3b=0 and b x-2y-3a=0 , where (a , b)!=(0,0) ,is

Find the equation of the line passing through the point of intersection of x + 2y =5 and x - 3y = 7, and passing through the point : (2, -3) .

Find the equation of the line passing through the point of intersection of x + 2y =5 and x - 3y = 7, and passing through the point : (0, -1).

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

If non-zero numbers a,b,c are in H.P., then the straight line x/a+ y/b+1/c=0 always passes through a fixed point. That point is :

The locus of the mid-points of the chords of the ellipse x^2/a^2+y^2/b^2 =1 which pass through the positive end of major axis, is.

Through the point P(alpha,beta) , where alphabeta>0, the straight line x/a+y/b=1 is drawn so as to form a triangle of area S with the axes. If a b >0, then the least value of S is

Find the equation of the straight line through the point P(a,b) parallel to the line x/a+y/b = 1 also find the intercepts made by it on the axes .