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CBSE Class 12-science Answered

what is a hyperbola
Asked by sheensvlog | 27 Mar, 2024, 10:15: PM
answered-by-expert Expert Answer

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

img

where b is

img

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