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AP EAMCET2013MathematicsHyperbola

If x=9 is a chord of contact of the hyperbola x^2-y^2=9 , then the equation of the tangent at one of the points of contact is

Options

  1. Ax+ 3 y+2=0
  2. B3 x+2 2 y-3=0
  3. C3 x- 2 y+6=0
  4. Dx- 3 y+2=0

Correct answer

B. 3 x+2 2 y-3=0

Step-by-step solution

Given that, x=9 is a chord of contact of hyperbola. aligned & x^2-y^2=9 & put x=9, 81-y^2=9 & y^2=72 & y=6 2 or -6 2 & aligned Points are (9,6 2 ) and (9,-6 2 ) Now, differentiating Eq. (i) w.r.t. x , we get aligned & 2 x-2 y d y d x =0 & d y d x = x y & at (9,6 2 ) ( d y d x )_ (9,6 2 ) = 9 6 2 = 3 2 2 & and at (9-6 2 ) ( d y d x )_ (9,-6 2 ) =- 3 2 2 & aligned Equation of tangent at (9,6 2 ) is aligned (y-6 2 ) & = 3 2 2 (x-9) 2 2 y-24 & =3 x-27 3 x-2 2 y-3 & =0 aligned and equation of tangent at (9,-6 2 ) is ali

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