Google Classroom
GeoGebraGeoGebra Classroom

orthogonal _Trajectory

Two family of curves x^2 - y*2 =c_1 and 2xy=c_2, when c_1≠0, the curve x^2 - y*2 =c_1 are rectangular hyperbolas with their foci on the x-axis or on the y axis according as c_1<0 or c_1>0 While the straight lines y = ± x , obtained when c_1=0 also belongs to the u-family ( serve as the common asymptotes of the hyperbolas of the family shared by S S Benchalli