Let $X\subset \mathbb{P}^m_k$ be a closed irreducible subvariety, and $f,g\in k[x_0,\dots,x_m]$ be homogenous polynomials of $\deg f=\deg g$.
Then we have parametrized hypersurfaces $V(af+bg)\subset \mathbb{P}^m$ for $(a:b)\in \mathbb{P}^1$.
Is the following subset of $\mathbb{P}^1$ closed in the Zariski topology?
$\{(a:b)\in \mathbb{P}^1~|~ X\subset V(af+bg)\}$
Moreover if it is true, how is this proposition generalized?