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If a tangent having slope 2 of the ellipse x 2 a 2 + y 2 b 2 = 1 is normal to the circle x 2 + y 2 + 4 x + 1 = 0, then the value of 4 a 2 + b 2 is equal to

Options

  1. A4
  2. B2
  3. C16
  4. D8

Correct answer

C. 16

Step-by-step solution

Equation of tangent is y = 2 x ± 4 a 2 + b 2 This is normal to the circle x 2 + y 2 + 4 x + 1 = 0 This tangent passes through - 2,0 0 = - 4 ± 4 a 2 + b 2 ⇒ 4 a 2 + b 2 = 16

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