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JEE Main202125 Jul 2021Morning ShiftMathematicsParabolaActual

Let a parabola P be such that its vertex and focus lie on the positive x -axis at a distance 2 and 4 units from the origin, respectively. If tangents are drawn from O ( 0 , 0 ) to the parabola P which meet P at S and R , then the area (in sq. units) of Δ S O R is equal to :

Options

  1. A16 2
  2. B16
  3. C32
  4. D8 2

Correct answer

B. 16

Step-by-step solution

From the diagram, clearly R S is latus-rectum ∵   V F = 4 - 2 2 + 0 - 0 2 = 2 = a ∴   R S = 4 a = 8 Now O F = 2 a = 4 So, the area of triangle O R S = 1 2 × 4 × 8 = 16

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