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The slope of the line touching both the parabolas y2= 4x and x2 = -32y is :

  • Option 1) (1/8)
  • Option 2) (2/3)
  • Option 3)(1/2)
  • Option 4)(3/2)

Answers (2)


As we learnt in

Equation of tangent -

y= mx+\frac{a}{m}

- wherein

Tengent to y^{2}=4ax is slope form.


  Tangent to Parabola y2=4x is y=mx+\frac{a}{m}

\Rightarrow y=mx +\frac{1}{m}.........................(1)

Tangent to parabola x2 =-32y

   y = mx - am2

\Rightarrow    y = mx + 8m2                                    --(2)

For some tangent 


\Rightarrow m=\frac{1}{2}

Option 1)


This option is Incorrect

Option 2)


This option is Incorrect

Option 3)


This option is correct

Option 4)


This option is Incorrect

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