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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

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

Grade:11

1 Answers

SAGAR SINGH - IIT DELHI
878 Points
13 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

b1c2−b2c1a1b2−a2b1c1a2−c2a1a1b2−a2b1            (obtain it)

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

a3b1c2−b2c1a1b2−a2b1+b3c1a2−c2a1a1b2−a2b1+c3=0

 a3b1c2−a3b2c1+a2b3c1−a1b3c2+a1b2c3−a2b1c3=0

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