JEE Main 2024 Mathematics question
Not in JEE syllabus
Two vertices of a triangle ABC are A(3, −1) and B(−2, 3), and its orthocentre is P(1, 1). If the coordinates of the point C are (α, β) and the centre of the circle circumscribing the triangle PAB is (h, k), then the value of (α + β) + 2(h + k) equals :
Answer: (C)
Solution
The slope of AB is −4/5, so the altitude from C (through P) has slope 5/4: y − 1 = (5/4)(x − 1). The slope of AP is (1 + 1)/(1 − 3) = −1, so BC has slope +1: y − 3 = x + 2. Solving, C = (21, 26), so α +
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