Diophantine Geometry: An Introduction
《Diophantine Geometry: An Introduction》 · 第 75 页 · Section A.4.3「Curves of Genus 0」，Theorem A.4.3.2
A conic defined over a number field $k$ has a $k$-rational point if and only if it has a rational point over all completions of $k$; this is a special case of the Hasse principle, valid for all quadratic forms.