$$\begin{gathered} \mathit{Q}\mathbf{ }\mathbf{1}\mathbf{.}\mathbf{ }The slope of the line touching both the parabolas y^2=4x and x^2= -32y is \\ \left(a\right) \frac{1}{2} \left(b\right) \frac{3}{2} \left(c\right) \frac{1}{8} \left(d\right) \frac{2}{3} \\ \mathit{Q}\mathbf{ }\mathbf{2}. The \tan gent at \left(1,7\right) to the curves x^2=y-6x touch the circle x^2+y^2+16x+12y+x=0 at \\ \left(a\right) \left(6,7\right) \left(b\right) \left(-6,7\right) \left(c\right) \left(6,-7\right) \left(d\right) \left(-6,-7\right) \end{gathered}$$