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AP EAMCET202423 May 2024Morning ShiftMathematicsHyperbolaActual

If y=x+ 2 is a tangent to the hyperbola x^2 a^2 - y^2 2 =1 , then equations of its directrices are

Options

  1. Ax= 3
  2. Bx= 8 3
  3. Cx= 2 3
  4. Dx= 4 3

Correct answer

B. x= 8 3

Step-by-step solution

Hyperbola: x^2 a^2 - y^2 2 =1 . Now, equation of tangent in slope form y=m x a^2 m^2-2 Comparing with given tangent line y=x+ 2 We get, m=1 and a^2-2=2 a^2=4e= 1+ 2 4 = 3 2 . So, equation of directrix x= a e = 8 3 .

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