  We establish the Hardy-Littlewood property (\`a la Borovoi-Rudnick) for
Zariski open subsets in affine quadrics of the form $q(x_1,\cdots,x_n)=m$,
where $q$ is a non-degenerate integral quadratic form in $n\geqslant 3$
variables and $m$ is a non-zero integer. This gives asymptotic formulas for the
density of integral points taking coprime polynomial values, which is a
quantitative version of the arithmetic purity of strong approximation property
off infinity for affine quadrics.
