JEE Main 2024 Mathematics question
Let S be the focus of the hyperbola , on the positive x-axis. Let C be the circle with its centre at A(√6, √5) and passing through the point S. If O is the origin and SAB is a diameter of C then the square of the area of the triangle OSB is equal to -
Answer: 40
Solution
c² = 3 + 5 = 8, so S = (2√2, 0). B = 2A − S = (2√6 − 2√2, 2√5). Area of OSB = ½·|OS|·|| = ½(2√2)(2√5) = 2√10, so its square is 40.