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-

Prove that the line x(a+2b) + y (a-3b)=a-b passes through a fixed point for different values of a and b . Also find the fixed point.

Show that the lines represented by x(a+3b)+y(2a-b)=5a+b pass through a fixed point for different values of a and b .

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.

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 slope of the line passing through the points (a^(2),b)and (b^(2),a) is

The common chord of the circle x^2+y^2+6x+8y-7=0 and a circle passing through the origin and touching the line y=x always passes through the point. (a) (-1/2,1/2) (b) (1, 1) (c) (1/2,1/2) (d) none of these

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

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

If a , b ,c are in harmonic progression, then the straight line ((x/a))+(y/b)+(l/c)=0 always passes through a fixed point. Find that point.

Let L be the line belonging to the family of straight lines (a+2b) x+(a-3b)y+a-8b =0, a, b in R, which is the farthest from the point (2, 2). If L is concurrent with the lines x-2y+1=0 and 3x-4y+ lambda=0 , then the value of lambda is