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JEE Main20207 Jan 2020Evening ShiftMathematicsEllipseActual

If 3 x + 4 y = 12 2 is a tangent o the ellipse x 2 a 2 + y 2 9 = 1 for some a ∈ R , then the distance between the foci of the ellipse is

Options

  1. A2 7
  2. B4
  3. C2 5
  4. D2 2

Correct answer

A. 2 7

Step-by-step solution

3 x + 4 y = 12 2 ⇒ 4 y = - 3 x + 12 2 ⇒ y = - 3 4 x + 3 2 Condition of tangency c 2 = a 2 m 2 + b 2 18 = a 2 ∙ 9 16 + 9 a 2 ∙ 9 16 = 9 a 2 = 16 a = 4 e = 1 - b 2 a 2 = 1 - 9 16 = 7 4 ∴ a e = 7 4 ∙ 4 = 7 ∴ Focus are ± 7 , 0 ∴ Distance between foci = 2 7

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