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Most Important Selected Qs for JEE AdvancedMathematicsHyperbola

Paragraph: An asymptote to a curve is a straight line which tends to be become tangent when point of contact approaches to infinity. Let the equation of hyperbola is S =0 , then the equation of its asymptotes is S + =0 , which will be pair of lines. On the basis of above information answer the following : Question: The equation of hyperbola whose asymptotes are the lines 3 x-4 y+7=0 and 4 x+3 y+1=0 and which passes t

Options

  1. A12 x^2-12 y^2-7 x y+31 x+17 y=0
  2. B12 x^2-12 y^2+7 x y+31 x+17 y+25=0
  3. C12 x^2-12 y^2+7 x y-31 x-17 y-11=0
  4. D12 x^2-12 y^2-7 x y+31 x+17 y-11=0

Correct answer

D. 12 x^2-12 y^2-7 x y+31 x+17 y-11=0

Step-by-step solution

Equation of hyperbola whose asymptotes are 3 x-4 y+7=0 and 4 x+3 y+1=0 will be (3 x-4 y+7)(4 x+3 y+1)+ =0 If it passes though (2,3) , then =-18 So hyperbola will be aligned & (3 x-4 y+7)(4 x+3 y+1)-18=0 & 12 x^2-12 y^2-7 x y+31 x+17 y-11=0 aligned

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