JEE Advanced 2009 Mathematics question
The locus of the orthocentre of the triangle formed by the lines
(1 + p)x - py + p(1 + p) = 0,
(1 + q)x - qy + q(1 + q) = 0,
and y = 0, where p ≠ q, is
Answer: (D)
Solution
The first two lines meet y = 0 at (−p, 0) and (−q, 0). Subtracting suitable multiples, their intersection is A = (pq, (1 + p)(1 + q)). The altitude from A is the vertical line x = pq. The altitude from (−p, 0) is perpendicular
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