Question

The straight lines given by x(a+2b)+y(a+3b)=a+b for different values of a and b passes through a fixed point. The coordinates of the fixed point are

• A. (2, -1)
• B. (2, 1)
• C. (-2, 1)
• D. (-2, -1)

Answer 1

The correct option is A (2, -1)

The given equation can be written as
a(x+y-1)+b(2x+3y-1)=0
$\Rightarrow (x+y-1)+\lambda (2x+3y-1)=0,\mathrm{where}\lambda =\frac{b}{a}\mathrm{This}\mathrm{is}\mathrm{of}\mathrm{the}\mathrm{form}{L}_1+{\mathrm{\lambda L}}_2=0$
$\mathrm{which}\mathrm{represents}a\mathrm{line}\mathrm{passing}\mathrm{through}\mathrm{the}\mathrm{point}\mathrm{of}\mathrm{intersection}\mathrm{of}\mathrm{the}\mathrm{lines}x+y-1=0\mathrm{and}2x+3y-1=0$
This gives the fixed point (2, -1).