A line L intersects the lines 3 x-2 y-1=0 and x+2 y+1=0 at the points A and B . If the point (1,2) bisects the line segment AB and x a + y b =1 is the equation of the line L. then a+2 b+1=

Step-by-step solution

Let point of intersection A (x₁, y₁ ) and B (x₂, y₂ ) x₁+x₂ 2 =1 x₂=2-x₁ y₁+y₂ 2 =2 y₂=4-y₁ A lies on 3 x-2 y-1=0 3 x₁-2 y₁-1=0 ....(i) and B lies on x+2 y+1=0 (2-x₁ )+2 (4-y₁ )+1=0 x₁+2 y₁-11=0 .....(ii) On solving equation (i) and (ii), we get x₁=3, y₁=4 x₂=-1, y₂=0 So, point A (3,4) and B (-1,0) Equation of line L i.e., AB : y-4= 4-0 3+1 (x-3) x-y+1=0 x -1 + y 1 =1 , Compare with x a + y b =1 we get a=-1 and b=1 Now, a+2 b+1=-1+2+1=2