# 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 $$X \cap \Pi$$?