1) x-2y-6=0 and 3x+y-4=0 and ax+4y+a2 =0 are concurrent then a 2 is ?? a) 2 b)4 c)-1/2 d)-4 e)0 2) point (a+1,1) , (2a+1,3) and (2a+2,2a) are collinear then value of a is a) 2 b)4 c)-1/2 d)-4 e)0 3)line x+y-1-a=0 passing through intersection of x-y+1=0 and 3x+y-5=0 are perpendicular to one of them find value of a? a) 2 b)4 c)-1/2 d)-4 e)0 4)if line y-x-1+a=0 is equally inclined to axes and equidistant from points(1,-2) and (3,4) then a is? a) 2 b)4 c)-1/2 d)-4 e)0

SAGAR SINGH - IIT DELHI
879 Points
12 years ago

Dear student,

Let the three given lines be

a1x+b1y+c1=0                                                                        ...(i)

a2x+b2y+c2=0                                                                         ..(ii)

a3x+b3y+c3=0                                                                        ...(iii)

For the given lines to be concurrent, no two of these lines can be parallel or coincident

b1a1=b2a2=b3a3                                                                         ...(iv)

and the point of intersection of any two lines must lie on the third. The point of intersection of (i) and (ii) is

b1c2b2c1a1b2a2b1c1a2c2a1a1b2a2b1            (obtain it)

This point must lie on the third line, so we must have

a3b1c2b2c1a1b2a2b1+b3c1a2c2a1a1b2a2b1+c3=0

a3b1c2a3b2c1+a2b3c1a1b3c2+a1b2c3a2b1c3=0