Let B and C are points of intersection of the parabola y = x 2 and the circle x 2 + y - 2 2 = 8 . The area of the triangle O B C , where O is the origin, is

Question

Let B and C are points of intersection of the parabola y = x 2 and the circle x 2 + y - 2 2 = 8 . The area of the triangle O B C , where O is the origin, is, 2, 4, 6, 8

MARKS App · Accepted Answer

Solving y = x 2 and x 2 + y - 2 2 = 8 we get, y + y - 2 2 = 8 ⇒ y 2 - 3 y - 4 = 0 ⇒ y = - 1,4 ⇒ y = 4 { y ≠ - 1 otherwise x is not defined} ⇒ x 2 = 4 ⇒ x = ± 2 Let, B = - 2,4 , C = 2,4 Now, the area of Δ O B C = 1 2 × 4 × 4 = 8 units

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