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AP EAMCET2010MathematicsHyperbola

The equation of the hyperbola which passes through the point (2,3) and has the asymptotes 4 x+3 y-7=0 and x-2 y-1=0 is

Options

  1. A4 x^2+5 x y-6 y^2-11 x+11 y+50=0
  2. B4 x^2+5 x y-6 y^2-11 x+11 y-43=0
  3. C4 x^2-5 x y-6 y^2-11 x+11 y+57=0
  4. Dx^2-5 x y-y^2-11 x+11 y-43=0

Correct answer

C. 4 x^2-5 x y-6 y^2-11 x+11 y+57=0

Step-by-step solution

Since, the equation of the hyperbola differs from that of the joint equations of the tangents by a constant, therefore the equation of the hyperbola will be of the form (4 x+3 y-7)(x-2 y-1)+k=0 ...(i) Since, the hyperbola passes through the point (2,3) . (8+9-7)(2-6-1)+k=0 (10)(-5)+k=0,-50+k=0 k=50 Hence, from Eq. (i) (4 x+3 y-7)(x-2 y-1)+50=04 x^2+3 x y-7 x-8 x y-6 y^2+14 y-4 x-3 y+7+50=04 x^2-5 x y-6 y^2-11 x+11 y+57=0

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