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-

If x^(2)+(a-b) x+(1-a-b)=0, a, b in R has unequal roots for all values of b, then

If the straight line ax + by + c =0 always passes thorugh ( 1, - 2) , then a,b,c, are in :

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 :

If the straight line ax +by+c=0 always passes through (1,-2) then a,b,c are in

The line parallel to the x axis and passing through the intersection of the lines ax+2by+3b=0 and bx -2ay-3a=0 where (a,b) ne (0,0) is

The normal to the curve x = a (1+cos theta), y = a sin theta at theta always passes through the fixed point

The plane passing through the point (a, b, c) and parallel to the plane x + y + z = 0 is:

The lines a x+b y=c, b x+c y=a and c x+a y=b are concurrent, if

The ratio in which the line segment (a_(1), b_(1)) and B (a_(2), b_(2)) is divided by Y-axis is

If the line (x)/(a)+(y)/(b)=1 passes through the points (2,-3) and (4,-5), then (a, b) is