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The equation of a common tangent to the curves, y^{2}=16x and xy=-4, is:

 

  • Option 1)

    x-y+4=0

  • Option 2)

    x+y+4=0

  • Option 3)

    x-2y+16=0

  • Option 4)

    2x-y+2=0

 

Answers (1)

Equation of tangent to parabola, y^{2}=16x is y=mx+\frac{4}{m}.............(1)

It is tangent to xy=-4....................(2)

Solving (1) and (2) we will get 

x(mx+\frac{4}{m})+4=0

For tangent \Delta =0=> \frac{16}{m^{2}}-16m=0=> m^{3}=1=> m=1

\therefore Putting m = 1 in eqn (1)

=> equation of common tangent is y=x+4

                                             =>   x-y+4=0


Option 1)

x-y+4=0

Option 2)

x+y+4=0

Option 3)

x-2y+16=0

Option 4)

2x-y+2=0

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Vakul

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