JEE Main 2024 Mathematics question
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 .
Answer: 16
Solution
For the second triangle the centroid G = (2O + H)/3 = (0, 0). So the first triangle has its orthocentre at the origin. The lines 2x + 3y = 1 and x + 2y = 1 meet at P(−1, 1); OP ⊥ third side
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