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JEE Advanced2012MathematicsHyperbolaActual

Tangents are drawn to the hyperbola x² 9 - y² 4 =1 , parallel to the straight line 2 x-y=1 . The points of contact of the tangents on the hyperbola are

Options

  1. A( 9 2 2 , 1 2 )
  2. B(- 9 2 2 ,- 1 2 )
  3. C(3 3 ,-2 2 )
  4. D(-3 3 , 2 2 )

Correct answer

A. ( 9 2 2 , 1 2 )

Step-by-step solution

If slope of tangents to hyperbola x² a² - y² b² =1 is m , then equations of tangent to the hyperbola is y=m x a² m²-b² with the points of contact ( a² m . . a² m²-b² a² m²-b² ) Tangent to hyperbola x² 9 - y² 4 =1 is parallel to 2 x-y=1 , Slope of tangent =2 Points of contact are ( 9 2 9 4-4 , 4 9 4-4 ) i.e. ( 9 2 2 , 1 2 ) and ( -9 2 2 , -1 2 )

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