Congruences of ruled quadrics with two double focal surfaces
In three-dimensional projective space P<sub>3</sub> two-parametric families (congruences) V<sub>2</sub> of rouled non-degenerates quadrics Q are investigated. It is proved that such congruences exist and with arbitrariness of five arbitraries functions of two arguments are defined. Using computer-program [1] four subclasses of such congruences are considered. If points A<sub>1</sub> and A<sub>2</sub> of intersection of lines A<sub>0</sub>A<sub>1</sub>, A<sub>3</sub>A<sub>1</sub> and A<sub>0</sub>A<sub>2</sub>, A<sub>3</sub>A<sub>2</sub> of quadric QV are also focal points than (A<sub>0</sub>) and (A<sub>3</sub>) are double focal surfaces it is istablished.