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AP EAMCET202422 May 2024Evening ShiftMathematicsHyperbolaActual

The line 21 x+5 y=k touches the hyperbola 7 x^2-5 y^2= 232 then k=

Options

  1. A116
  2. B232
  3. C58
  4. D110

Correct answer

A. 116

Step-by-step solution

The line A x+ B y+ C =0 touches the hyperbola x^2 a^2 - y^2 b^2 =1 if C ^2=a^2 ~A ^2-b^2 ~B ^2 ...(i) Now, given line is 21 x+5 y=k and hyperbola 7 x^2-5 y^2=232 x^2 ( 232 7 ) - y^2 ( 232 5 ) =1 So, from (i) we have k^2= 232 7 (21)^2- 232 5 (5)^2 k=116

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