ends of minor axis ( , ± ) . Ends of major axis ( , ± ), ends of minor axis ( ± , ) . Length of major axis , foci ( ± , ) . Length of minor axis , foci ( , ± ).
. Foci ( ± , ), a = . b = , c = , centre at the origin; foci on the x axis. .
Centre at ( , ), major axis on the y -axis and passes through the points ( , ) and ( , ). . Major axis on the x -axis and passes through the points ( , ) and ( , ). .
Hyperbola Definition A hyperbola is the set of all points in a plane, the difference of whose distances from two fixed points in the plane is a constant. MATHEMATICS The term “ difference ” that is used in the definition means the distance to the farther point minus the distance to the closer point. The two fixed points are called the foci of the hyperbola. The mid-point of the line segment joining the foci is called the centre of the hyperbola .
The line through the foci is called the transverse axis and the line through the centre and perpendicular to the transverse axis is called the conjugate axis . The points at which the hyperbola intersects the transverse axis are called the vertices of the hyperbola (Fig . ). We denote the distance between the two foci by c , the distance between two vertices (the length of the transverse axis) by a and we define the quantity b as b = c – a Also b is the length of the conjugate axis (Fig .
). To find the constant P F – P F : By taking the point P at A and B in the Fig . , we have BF – BF = AF – AF (by the definition of the hyperbola) BA +AF – BF = AB + BF – AF i.e., AF =