Part a)
<a href="http://www.codecogs.com/eqnedit.php?latex=y=kx^2 \textrm{ has tangent }8x-y-4=0\\ ~\\ $Solving simultaneously, we have $ 8x-kx^2-4=0\\ $Now, for the line to be a tangent, it intersects the parabola at one point, so there is only one solution to the above equation, i.e. $\Delta...