CBSE Class 12-science Answered
A hyperbola is the locus of all those points in a plane such that the difference in their distances
from two fixed points in the plane is a constant.
The fixed points F1 and F2 in the above figure are referred to as foci .
The above figure represents a hyperbola such that P1F2 – P1F1 = P2F2 – P2F1 = P3F1 – P3F2 is a constant.
Let O bt the middle point of line joining F1 and F2 . Let us consider the point O is at origin of coordinate system.
and the line joining F1 and F2 is on x-axis . Point of intersection of hyperbola and x-axis is called vertex and
center of hyperbola is nid point of line joining F1 and F2 . In the figure , origin is center of hyperbola.
Each vertex is at equal distance a from origin as shown in figure.
Coordinates of foci are (-c, 0 ) and (c, 0 ) .
The ratio between distance a from center of hyperbola to vertex to the distance c from center of hyperbola to focus
is called eccentricity e
e = c/a > 1
Equation of hyperbola is
where b is