JEE Main 2024 Mathematics question
Three points O(0, 0), P(a, a²), Q(−b, b²), a > 0, b > 0, are on the parabola y = x². Let be the area of the region bounded by the line PQ and the parabola, and be the area of the triangle OPQ. If the minimum value of is , gcd(m, n) = 1, then m + n is equal to
Answer: 7
Solution
S₁ = (a + b)³/6 and S₂ = ab(a + b)/2, so S₁/S₂ = (a + b)²/(3ab) ≥ 4/3; m + n = 7.