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AP EAMCET2016MathematicsHyperbola

The values of m for which the line y=m x+2 becomes a tangent to the hyperbola 4 x^2-9 y^2=36 is

Options

  1. A2 3
  2. B2 2 3
  3. C8 9
  4. D4 2 3

Correct answer

B. 2 2 3

Step-by-step solution

We have, line, y=m x+2 ... (i) Hyperbola, 4 x^2-9 y^2=36... (ii) On solving eqs. (i) and (ii), we get x^2 (4-9 m^2 )-36 m x-72=0 Since, this line is a tangent of hyperbola array ll & D = b ^2-4 ac =0 & (36 m)^2+4 72 (4-9 m^2 )=0 & 36 36 m^2+4 36 2 (4-9 m^2 )=0 & 9 m^2+8-18 m^2=0 & 9 m^2=8 & m^2= 8 9 & m^2= 8 9 = 2 2 3 array

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