2x+3y−1=0x+2y−1=0ax+by−1=0 
(36−6,38−8)=(0,0)
ax+by−1=0(−1−01−0)(b−a)=−1⇒−a=b⇒ax−ay−1=0ax−a(1−32x)−1x(a+32a)=3ax=5aa+32(5aa+3)+3y−1=0y=31−5a2a+6=3×5a3a−6y=5aa−2(5aa+3)(5aa−2)=2⇒a−2=2a+6a=−8 b=8−8x+8y−1=0∣a−b∣=16
JEE Main 2024 — Mathematics Coordinate Geometry
If the orthocentre of the triangle formed by the lines 2x+3y−1=0,x+2y−1=0 and ax+by−1=0, is the centroid of another triangle, whose circumcentre and orthocentre respectively are (3,4) and (−6,−8), then the value of ∣a−b∣ is_______
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