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NTA Abhyas JEE Main2020MathematicsEllipsePractice

From the point P 3,4 pair of tangents P A and P B are drawn to the ellipse x 2 16 + y 2 9 = 1 . If A B intersects y -axis at C and x -axis at D , then O C · O D is equal to (where O is the origin)

Options

  1. A9
  2. B18
  3. C8
  4. D12

Correct answer

D. 12

Step-by-step solution

Equation of the chord of contact of the tangents from point P to the given ellipse is 3 x 16 + 4 y 9 = 1 ∴ C 0 , 9 4 ,   D 16 3 , 0 ⇒ O C × O D = 9 4 × 16 3 = 12

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