Find The Hyperbola Whose Asymptotes Are 2x – Y = 3 And 3x + Y – 7 = 0 And Which Passes Through The Point (1, 1).

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Find the hyperbola whose asymptotes are 2x – y = 3 and 3x + y – 7 = 0 and which passes through the point (1, 1).


Correct option is


      The equation of the hyperbola differs from the equation of the asymptotes by a constant.

 The equation of the hyperbola with asymptotes 3x + y – 7 = 0   

     and 2x – y = 3 is

     (3x + y – 7)(2x – y – 3) + k = 0

It passes through (1, 1)  k = – 6

Hence the equation of the hyperbola is

      (3x + y – 7)(2x – y – 3) = 6



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