A variable straight line AB intersecting the x and y-axes atA and B always passes through a fixed point `(alpha, beta)`. Find thelocus of the point dividing AB in the ratio 2:1.

A variable straight line AB intersecting the x and y-axies at A and B always passes through a fixed point (alpha,beta) . Find the locus of the point dividing AB in the ratio 2:1 .

A variable straight line AB intersecting the x and y-axes at A and B always pases the point fixed point (alpha,beta). Find thelocus of the point dividing AB in the ratio 2:1.

A variable line passes through the fixed point (alpha,beta) . The locus of the foot of the perpendicular from the origin on the line is

A variable line passes through the fixed point (alpha,beta) . The locus of the foot of the perpendicular from the origin on the line is,

Show that the straight line (a + 2b) x + (a -3b)y + b -a = 0 always passes through a fixed point. Find the co-ordinate of that point.

A moving straight line always passes through a fixed point (alpha , beta) . Prove that the locus of the middle point of the portion of the line intercepted between the axes is (alpha)/(x)+(beta)/(y) = 2 .

Show that the straight line (a+2b)x+(a-3b)y+b-a=0 always passes through a fixed point , find the cootdinates of that fixed point.

A moving straight line always passes through a fixed point (alpha,beta) .Prove that the locus of the middile point of the portion of the line intercepted between the axes is alpha/x+beta/y=2