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The equation of the common tangent to the curves y2 = 8x and xy = - 1 is

  • (a) 3y = 9x + 2
  • (b) y = 2x + 1
  • (c) 2y = x + 8
  • (d) y = x + 2
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Correct option is (d) y=x+2 

Explaination::

tangents to the curve y2=8x is y=mx+2/m , so it must satisfy xy=-1 

\(x({mx+\frac{2}{m}})=-1\) 

\(mx^2+\frac{2}{m}x+1=0 ,\) 

since it has equal roots , therefore D=0

\(\frac{4}{m^2}-4m=0\) 

\(m^3=1 \) 

m=1

therefore , the equation of commom tangent is y=x+2

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