Show that the straight lines given by `x(a+2b)+y(a+3b)= a + b` for different values of `a and b` pass through a fixed point.

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.

Consider the equation y-y_1=m(x-x_1) . If ma n dx_1 are fixed and different lines are drawn for different values of y_1, then (a) the lines will pass through a fixed point (b) there will be a set of parallel lines (c) all the lines intersect the line x=x_1 (d)all the lines will be parallel to the line y=x_1

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.

If a and b are two arbitrary constants, then prove that the straight line (a-2b)x+(a+3b)y+3a+4b=0 will pass through a fixed point. Find that point.

A variable straight line passes through the point of intersection of the straight lines (x)/(a)+(y)/(b)=1 and (x)/(b)+(y)/(a)=1 and intersects the axes at P and Q. Find the locus of midpoint of PQ.

If the straight line (x)/(a) + (y)/(b) = 1 is parallel to the line 4x + 3y = 6 and passes through the point of intersection of the lines 2x - y - 1 = 0 and 3x - 4y + 6 = 0 ,find the values of a and b .

The distance of the straight line a(x-a)+b(y-b)=0 from the origin is -

If a , b , c are in A . P ., then the straight line ax + 2 by + c = 0 will always pass through a fixed point whose coordinates are _

A variable straight line passes through the point of intersection of the staright lines x/a+y/b=1 and x/b+y/a=1 and intersects the axes at P and Q.Find the locus of mid-point of Pq.

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 .