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JEE Main201912 Apr 2019Evening ShiftMathematicsHyperbolaActual

The equation of a common tangent to the curves, y 2 = 16 x and x y = - 4 , is:

Options

  1. Ax - 2 y + 16 = 0
  2. Bx - y + 4 = 0
  3. C2 x - y + 2 = 0
  4. Dx + y + 4 = 0

Correct answer

B. x - y + 4 = 0

Step-by-step solution

A tangent to the parabola y 2 = 16 x can be written as: y = m x + 4 m …. (1) It will touch the hyperbola x y =   – 4 ,   if the quadratic x m x + 4 m = – 4 has coincident roots, ⇒ m 2 x 2 + 4 x + 4 m = 0 ,   D ≡ 16 - 16 m 3 = 0 ⇒ m = 1 ⇒ Equating of common tangent will be y = x + 4 ⇒ x - y + 4 = 0

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