Discussion Forum

 The slope of the line touching both the parabola   $y^{2}=4x$    and $x^{2}=-32y$ is 

Answer:

Explanation:

 Let the tangent  to parabola be y=mx+a/m, If it touches the other  curve, then D=0, to get the value of m 

 For parabola, $y^{2}=4x$ 

  Let y=mx+1/m  be tangent line and it touches the parabola  $x^{2}=-32y$

   $\therefore$   $ x^{2}=-32\left(mx+\frac{1}{m}\right)$

$\Rightarrow $     $x^{2}+32mx+\frac{32}{m}=0$

$\therefore$     D=0

$\therefore$    $(32m)^{2}-4.\left(\frac{32}{m}\right)=0$

    $\Rightarrow $                    $m^{3}=\frac{1}{8}$

      $\therefore$                      m$=\frac{1}{2}$