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Two lines L 1 and L 2 of slope 1 are tangent to y 2 = 4 x and x 2 + 2 y 2 = 4 respectively, such that the distance d units between L 1 and L 2 is minimum, then the value of d is equal to

Options

  1. A3 - 1 2
  2. B3 + 1 2
  3. C2 - 1
  4. D3 + 2

Correct answer

A. 3 - 1 2

Step-by-step solution

y = x + 1 is a tangent to y 2 = 4 x y = x ± 4 + 2 is a tangent to x 2 4 + y 2 2 = 1 ⇒ Minimum distance will be between the parallel lines y = x + 6 and y = x + 1 ⇒ d = 6 - 1 2 = 3 - 1 2 units

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