Equation of a common tangent  to the parabola y2=4x and the hyperbolaxy=2 is

Equation of a common tangent  to the parabola y2=4x and the hyperbolaxy=2 is

  1. A

    4x+2y+1=0

  2. B

    x+2y+4=0

  3. C

    x+y+1=0

  4. D

    x2y+4=0

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    Solution:

    Let the equation of tangent to parabola

    y2=4x be y=mx+1/m                                        …(i)

    It is also a tangent to hyperbola xy = 2.

     xmx+1m=2                                                 [From (i)]

     x2m+x/m2=0

    Now, D=01/m2+8m=0m=1/2

    Equation of tangent is y=12x2

     2y+x+4=0

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