The equation of a tangent to the hyperbola 4×2−5y2=20 parallel to the line x – y = 2 is

The equation of a tangent to the hyperbola 4x25y2=20 parallel to the line x - y = 2 is

  1. A

    xy3=0

  2. B

    xy+9=0

  3. C

    xy+1=0

  4. D

    xy+7=0

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    Solution:

    Given, equation of hyperbola is x25y24=1

    Now, equation of the tangent to the hyperbola is y=mx±a2m2b2                              (i)

    Since, the tangent is parallel to xy=2

     Slope of the tangent is 1

     (i) becomes; y=x±54y=x±1

    y=x+1 or y=x1

    xy+1=0 or xy1=0

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