Lines on hypersurfaces

Let $ X$ be a hypersurface in a projective space and let $ P \in X$ . Further, let $ \Pi$ be a hyperplane not passing through $ P$ . If $ \{l_i \mid i \in I\}$ be the set of all the lines passing through $ P$ . My question is whether $ (\cup_{i \in I} l_i) \cap \Pi$ a Zariski closed subset of $ X \cap \Pi$ ?