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Most Important Selected Qs for JEE AdvancedMathematicsHyperbola

Circles are drawn on chords of the rectangular hyperbola xy = c ^2 parallel to the line y = x as diameters All such circles pass through two fixed points whose coordinates are (A)(C, c)

Options

  1. A(c, c)
  2. B(c,-c)
  3. C(-c, c)
  4. D(-c,-c)

Correct answer

D. (-c,-c)

Step-by-step solution

1 t₁ t₂ =-1 ; (x-x t₁ ) (x-c t₂ )+ (y- c t₁ ) (y- c t₂ )=1 [t₁ t₂=-1 ] (x^2+y^2-2 c )- (t₁+t₂ )(x-y)=0 S- L=0 Hence, we get (c, c) and (-c,-c)

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