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

  • Option 1)

    \frac{1}{8}

  • Option 2)

    \frac{2}{3}

  • Option 3)

    \frac{1}{2}

  • Option 4)

    \frac{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 

8m^{2}=\frac{1}{m}

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


Option 1)

\frac{1}{8}

This option is Incorrect

Option 2)

\frac{2}{3}

This option is Incorrect

Option 3)

\frac{1}{2}

This option is correct

Option 4)

\frac{3}{2}

This option is Incorrect

N neha

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