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