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JEE Main201912 Apr 2019Morning ShiftMathematicsHyperbolaActual

Let P be the point of intersection of the common tangents to the parabola y 2 = 12 x and the hyperbola 8 x 2 - y 2 = 8 . If S and S ' denote the foci of the hyperbola where S lies on the positive x -axis then P divides S S ' in a ratio:

Options

  1. A5 : 4
  2. B2 : 1
  3. C13 : 11
  4. D14 : 13

Correct answer

A. 5 : 4

Step-by-step solution

Let m is slope of common tangent and an equation of tangent to hyperbola x 2 1 - y 2 8 = 1 is y = m x ± 1 ⋅ m 2 - 8             . . . 1 equation of tangent to parabola y 2 = 12 x is y = m x + 3 m               . . . 2 ∵   1   &   2 is same ∴     ± m 2 - 8 = 3 m ⇒ m 4 - 8 m 2 - 9 = 0 ⇒ m 2 = - 1 (Reject) ⇒ m 4 - 8 m 2 - 9 = 0 ⇒ m 2 = 9 ⇒ m = ± 3 ∵ equation

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