The importance of this research lies in notifying analytic geometry principles in Lobachevsky plane which differ from the famous principles in Euclidean plane . In this research, length of curves with constant curvature , length of a circle and an arc length of it opp to a central angle has been found . Moreover , it has been reached to a formula to express the distance between two points ; then writing a line equation passes coordinates principle , a line equation that doesn`t pass coordinates principle and a circle equation. We coordinates which have used for that Beltrami made the formulas simpler.