# Polar divisor contains no hyperplane when degree $d\geq 3$

Let $$X\subset \mathbb P^n=\mathbb P^n_\mathbb C$$ $$(n>3)$$ be a smooth hypersurface of degree $$d\geq 3$$, defined by a homogeneous polynomial $$F$$. Let $$a=[a_0:\ldots:a_n]\in \mathbb P^n$$ be any closed point, then the corresponding polar divisor with pole $$a$$ is defined to be the zero locus of $$\sum a_i \partial_iF=0$$ in $$\mathbb P^n$$. I believe the following statement is always true but I did not find how to prove:

there is no polar divisor contains a hyperplane in $$\mathbb P^n$$.

There is a very geometric interpretation: if a hyperplane contains in some polar divisor, then the nearby hyperplane sections of $$X$$ are all isomorphic. This phenomenon should not occur when degree is at least $$3$$. (In the case of degree $$2$$, a polar divisor is always a hyperplane, which should be interpreted as all smooth quadratic surfaces are isomorphic. This is also the classic pole and polar.)