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JEE Main202125 Feb 2021Evening ShiftMathematicsEllipseActual

If the curve x 2 + 2 y 2 = 2 intersects the line x + y = 1 at two points P and Q , then the angle subtended by the line segment P Q at the origin is

Options

  1. Aπ 2 - tan - 1 1 3
  2. Bπ 2 + tan - 1 1 3
  3. Cπ 2 + tan - 1 1 4
  4. Dπ 2 - tan - 1 1 4

Correct answer

C. π 2 + tan - 1 1 4

Step-by-step solution

Homogenising x 2 + 2 y 2 - 2 x + y 2 = 0 ⇒ - x 2 - 4 x y = 0 ⇒ x 2 + 4 x y = 0 Lines are x = 0 and y = - x 4 ∴ Angle between lines = π 2 + tan - 1 1 4 option 3

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