the line p(p²+1)x-y+q=0 and (p²+1)²x+(p²+1)y+2q=0 are perpendicular to the common line for ?

Dear student

if the to lines are perpendicular to a common line

then those two lines are parallel

slopes are equal

$$\begin{gathered} \frac{p(p^2+1)}{1}=-\frac{(p^2+1{)}^2}{(p^2+1)} \\ or p=-1 \end{gathered}$$

Regards