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The locus of middle points of chords of hyperbola 3 x 2 - 2 y 2 + 4 x - 6 y = 0 parallel to y = 2 x is

Options

  1. A3 x - 4 y = 4
  2. B3 y - 4 x + 4 = 0
  3. C4 x - 3 y = 3
  4. D3 x - 4 y = 2

Correct answer

A. 3 x - 4 y = 4

Step-by-step solution

Let ( h , k ) is mid point of chord. Then, its equation is T = S 1 ∴ 3 h x - 2 k y + 2 x + h - 3 y + k = 3 h 2 - 2 k 2 + 4 h - 6 k x 3 h + 2 + y - 2 k - 3 = 3 h 2 - 2 k 2 + 2 h - 3 k Since, this line is parallel to y = 2 x 3 h + 2 2 k + 3 = 2 ⇒ 3 h - 4 k = 4 Thus, locus of point is 3 x - 4 y = 4

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