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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
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
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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