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Manipal MET2012MathematicsParabola

The equation of the common tangent to the curves y^2=8 x and x y=-1 is

Options

  1. A3 y=9 x+2
  2. By=2 x+1
  3. C2 y=x+8
  4. Dy=x+2

Correct answer

D. y=x+2

Step-by-step solution

Tangent to the curve y^2=8 x is y=m x+ 2 m . So, it must satisfy x y=-1 x (m x+ 2 m )=-1 m x^2+ 2 m x+1=0 Since, it has equal roots. D=0 array ll & 4 m^2 -4 m=0 & m^3=1 m=1 array So, equation of common tangent is y=x+2 .

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