HYPERBOLA FORMULA
In simple sense, hyperbola looks similar to to mirrored parabolas. The two halves are called the branches. When the plane intersect on the halves of a right circular cone angle of which will be parallel to the axis of the cone, a parabola is formed.
A hyperbola contains: two foci and two vertices. The foci of the hyperbola are away from the hyperbola’s center and vertices. Here is an illustration to make you understand:
The equation for hyperbola is,
Where,
Let us learn the basic terminologies related to hyperbola formula:
MAJOR AXIS
The line that passes through the center, focus of the hyperbola and vertices is the Major Axis. Length of the major axis = 2a. The equation is given as:
MINOR AXIS
The line perpendicular to the major axis and passes by the middle of the hyperbola is the Minor Axis.
Length of the minor axis = 2b. The equation is given as:
ECCENTRICITY
The variation in the conic section being completely circular is eccentricity. It is usually greater than 1 for hyperbola. Eccentricity is
ASYMPTOTES
Two bisecting lines that is passing by the center of the hyperbola that doesn’t touch the curve is known as the Asymptotes. The equation is given as:
Directrix of a hyperbola
Directrix of a hyperbola is a straight line that is used in generating a curve. It can also be defined as the line from which the hyperbola curves away from. This line is perpendicular to the axis of symmetry. The equation of directrix is:
VERTEX
The point of the branch that is stretched and is closest to the center is the vertex. The vertex points are
Focus (foci)
On a hyperbola, focus (foci being plural) are the fixed points such that the difference between the distances are always found to be constant. The two focal points are:
Solved examples
Question: The equation of the hyperbola is given as:
Find the following: Vertex, Asymptote, Major Axis, Minor Axis and Directrix?
Solution:
Given,
The vertex point:
Asymptote
Major Axis
a = 9
Minor Axis
b = 7
Directrix
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