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The locus of the midpoint of the chords of the hyperbola x 2 25 - y 2 36 = 1 which passes through the point 2 , 4 is a hyperbola, whose transverse axis length (in units) is equal to

Options

  1. A16 5
  2. B4 3
  3. C8 5
  4. D61 25

Correct answer

A. 16 5

Step-by-step solution

The equation of the chord whose mid-point is ( h , k ) is T = S 1 ⇒ x h 25 - y k 36 = h 2 25 - k 2 36 Since it passes through 2 , 4 2 h 25 - 4 k 36 = h 2 25 - k 2 36 ⇒ h 2 - 2 h + 1 25 - k 2 - 4 k + 4 36 = 1 25 - 4 36 Hence, the locus of h , k is x - 1 2 16 9 - y - 2 2 64 25 = - 1 This is the equation of a hyperbola whose transverse axis length is 16 5 units

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