  We study an asymptotic formula for counting integral points over an equation
defined by a non-degenerated indefinite integral ternary quadratic form $f$
representing a non-zero integer $a$ such that $-a\cdot det(f)$ is square over a
number field. In particular, we prove that the finite part of this asymptotic
formula is given by the product of local density times $1-p^{-1}$ over all
finite primes $p$ over $\Bbb Z$.
