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The locus of a point which moves such that the difference of its distances from the points 5,0 and - 5,0 is 6 units is a conic, whose length of the latus rectum (in units) is equal to

Options

  1. A4
  2. B16 3
  3. C8
  4. D32 3

Correct answer

D. 32 3

Step-by-step solution

Because 6 < 5 - - 5 Hence, the locus is a hyperbola by definition. Let's assume the eccentricity, semi-transverse axis and the semi-conjugate axis of the hyperbola is e , a , and b respectively, then 2 a e = 10 Distance between focii - 5,0   &   5,0 = 10 = 2 a e & 2 a = 6 ⇒ e = 10 6 = 5 3 ⇒ 1 + b 2 a 2 = e 2 = 25 9 ⇒ b 2 a 2 = 25 9 - 1 = 16 9 ⇒ 2 b 2 a = 2 × 16 9 × a = 32 3 = length of the latus rectum

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